{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Dynamic factors and coincident indices\n", "\n", "Factor models generally try to find a small number of unobserved \"factors\" that influence a substantial portion of the variation in a larger number of observed variables, and they are related to dimension-reduction techniques such as principal components analysis. Dynamic factor models explicitly model the transition dynamics of the unobserved factors, and so are often applied to time-series data.\n", "\n", "Macroeconomic coincident indices are designed to capture the common component of the \"business cycle\"; such a component is assumed to simultaneously affect many macroeconomic variables. Although the estimation and use of coincident indices (for example the [Index of Coincident Economic Indicators](http://www.newyorkfed.org/research/regional_economy/coincident_summary.html)) pre-dates dynamic factor models, in several influential papers Stock and Watson (1989, 1991) used a dynamic factor model to provide a theoretical foundation for them.\n", "\n", "Below, we follow the treatment found in Kim and Nelson (1999), of the Stock and Watson (1991) model, to formulate a dynamic factor model, estimate its parameters via maximum likelihood, and create a coincident index." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Macroeconomic data\n", "\n", "The coincident index is created by considering the comovements in four macroeconomic variables (versions of these variables are available on [FRED](https://research.stlouisfed.org/fred2/); the ID of the series used below is given in parentheses):\n", "\n", "- Industrial production (IPMAN)\n", "- Real aggregate income (excluding transfer payments) (W875RX1)\n", "- Manufacturing and trade sales (CMRMTSPL)\n", "- Employees on non-farm payrolls (PAYEMS)\n", "\n", "In all cases, the data is at the monthly frequency and has been seasonally adjusted; the time-frame considered is 1972 - 2005." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:45:28.054936Z", "iopub.status.busy": "2023-12-14T14:45:28.054692Z", "iopub.status.idle": "2023-12-14T14:45:33.438738Z", "shell.execute_reply": "2023-12-14T14:45:33.437945Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "\n", "np.set_printoptions(precision=4, suppress=True, linewidth=120)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:45:33.442643Z", "iopub.status.busy": "2023-12-14T14:45:33.442181Z", "iopub.status.idle": "2023-12-14T14:45:37.041846Z", "shell.execute_reply": "2023-12-14T14:45:37.040763Z" } }, "outputs": [], "source": [ "from pandas_datareader.data import DataReader\n", "\n", "# Get the datasets from FRED\n", "start = '1979-01-01'\n", "end = '2014-12-01'\n", "indprod = DataReader('IPMAN', 'fred', start=start, end=end)\n", "income = DataReader('W875RX1', 'fred', start=start, end=end)\n", "sales = DataReader('CMRMTSPL', 'fred', start=start, end=end)\n", "emp = DataReader('PAYEMS', 'fred', start=start, end=end)\n", "# dta = pd.concat((indprod, income, sales, emp), axis=1)\n", "# dta.columns = ['indprod', 'income', 'sales', 'emp']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note**: in a recent update on FRED (8/12/15) the time series CMRMTSPL was truncated to begin in 1997; this is probably a mistake due to the fact that CMRMTSPL is a spliced series, so the earlier period is from the series HMRMT and the latter period is defined by CMRMT.\n", "\n", "This has since (02/11/16) been corrected, however the series could also be constructed by hand from HMRMT and CMRMT, as shown below (process taken from the notes in the Alfred xls file)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:45:37.045863Z", "iopub.status.busy": "2023-12-14T14:45:37.045326Z", "iopub.status.idle": "2023-12-14T14:45:37.048864Z", "shell.execute_reply": "2023-12-14T14:45:37.048086Z" } }, "outputs": [], "source": [ "# HMRMT = DataReader('HMRMT', 'fred', start='1967-01-01', end=end)\n", "# CMRMT = DataReader('CMRMT', 'fred', start='1997-01-01', end=end)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:45:37.052075Z", "iopub.status.busy": "2023-12-14T14:45:37.051578Z", "iopub.status.idle": "2023-12-14T14:45:37.055288Z", "shell.execute_reply": "2023-12-14T14:45:37.054683Z" } }, "outputs": [], "source": [ "# HMRMT_growth = HMRMT.diff() / HMRMT.shift()\n", "# sales = pd.Series(np.zeros(emp.shape[0]), index=emp.index)\n", "\n", "# # Fill in the recent entries (1997 onwards)\n", "# sales[CMRMT.index] = CMRMT\n", "\n", "# # Backfill the previous entries (pre 1997)\n", "# idx = sales.loc[:'1997-01-01'].index\n", "# for t in range(len(idx)-1, 0, -1):\n", "# month = idx[t]\n", "# prev_month = idx[t-1]\n", "# sales.loc[prev_month] = sales.loc[month] / (1 + HMRMT_growth.loc[prev_month].values)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:45:37.060487Z", "iopub.status.busy": "2023-12-14T14:45:37.058989Z", "iopub.status.idle": "2023-12-14T14:45:37.078339Z", "shell.execute_reply": "2023-12-14T14:45:37.077573Z" } }, "outputs": [], "source": [ "dta = pd.concat((indprod, income, sales, emp), axis=1)\n", "dta.columns = ['indprod', 'income', 'sales', 'emp']\n", "dta.index.freq = dta.index.inferred_freq" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:45:37.086177Z", "iopub.status.busy": "2023-12-14T14:45:37.083697Z", "iopub.status.idle": "2023-12-14T14:45:40.366662Z", "shell.execute_reply": "2023-12-14T14:45:40.365967Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dta.loc[:, 'indprod':'emp'].plot(subplots=True, layout=(2, 2), figsize=(15, 6));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Stock and Watson (1991) report that for their datasets, they could not reject the null hypothesis of a unit root in each series (so the series are integrated), but they did not find strong evidence that the series were co-integrated.\n", "\n", "As a result, they suggest estimating the model using the first differences (of the logs) of the variables, demeaned and standardized." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:45:40.371743Z", "iopub.status.busy": "2023-12-14T14:45:40.370230Z", "iopub.status.idle": "2023-12-14T14:45:40.407008Z", "shell.execute_reply": "2023-12-14T14:45:40.405921Z" } }, "outputs": [], "source": [ "# Create log-differenced series\n", "dta['dln_indprod'] = (np.log(dta.indprod)).diff() * 100\n", "dta['dln_income'] = (np.log(dta.income)).diff() * 100\n", "dta['dln_sales'] = (np.log(dta.sales)).diff() * 100\n", "dta['dln_emp'] = (np.log(dta.emp)).diff() * 100\n", "\n", "# De-mean and standardize\n", "dta['std_indprod'] = (dta['dln_indprod'] - dta['dln_indprod'].mean()) / dta['dln_indprod'].std()\n", "dta['std_income'] = (dta['dln_income'] - dta['dln_income'].mean()) / dta['dln_income'].std()\n", "dta['std_sales'] = (dta['dln_sales'] - dta['dln_sales'].mean()) / dta['dln_sales'].std()\n", "dta['std_emp'] = (dta['dln_emp'] - dta['dln_emp'].mean()) / dta['dln_emp'].std()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dynamic factors\n", "\n", "A general dynamic factor model is written as:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\Lambda f_t + B x_t + u_t \\\\\n", "f_t & = A_1 f_{t-1} + \\dots + A_p f_{t-p} + \\eta_t \\qquad \\eta_t \\sim N(0, I)\\\\\n", "u_t & = C_1 u_{t-1} + \\dots + C_q u_{t-q} + \\varepsilon_t \\qquad \\varepsilon_t \\sim N(0, \\Sigma)\n", "\\end{align}\n", "$$\n", "\n", "where $y_t$ are observed data, $f_t$ are the unobserved factors (evolving as a vector autoregression), $x_t$ are (optional) exogenous variables, and $u_t$ is the error, or \"idiosyncratic\", process ($u_t$ is also optionally allowed to be autocorrelated). The $\\Lambda$ matrix is often referred to as the matrix of \"factor loadings\". The variance of the factor error term is set to the identity matrix to ensure identification of the unobserved factors.\n", "\n", "This model can be cast into state space form, and the unobserved factor estimated via the Kalman filter. The likelihood can be evaluated as a byproduct of the filtering recursions, and maximum likelihood estimation used to estimate the parameters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model specification\n", "\n", "The specific dynamic factor model in this application has 1 unobserved factor which is assumed to follow an AR(2) process. The innovations $\\varepsilon_t$ are assumed to be independent (so that $\\Sigma$ is a diagonal matrix) and the error term associated with each equation, $u_{i,t}$ is assumed to follow an independent AR(2) process.\n", "\n", "Thus the specification considered here is:\n", "\n", "$$\n", "\\begin{align}\n", "y_{i,t} & = \\lambda_i f_t + u_{i,t} \\\\\n", "u_{i,t} & = c_{i,1} u_{1,t-1} + c_{i,2} u_{i,t-2} + \\varepsilon_{i,t} \\qquad & \\varepsilon_{i,t} \\sim N(0, \\sigma_i^2) \\\\\n", "f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \\eta_t \\qquad & \\eta_t \\sim N(0, I)\\\\\n", "\\end{align}\n", "$$\n", "\n", "where $i$ is one of: `[indprod, income, sales, emp ]`.\n", "\n", "This model can be formulated using the `DynamicFactor` model built-in to statsmodels. In particular, we have the following specification:\n", "\n", "- `k_factors = 1` - (there is 1 unobserved factor)\n", "- `factor_order = 2` - (it follows an AR(2) process)\n", "- `error_var = False` - (the errors evolve as independent AR processes rather than jointly as a VAR - note that this is the default option, so it is not specified below)\n", "- `error_order = 2` - (the errors are autocorrelated of order 2: i.e. AR(2) processes)\n", "- `error_cov_type = 'diagonal'` - (the innovations are uncorrelated; this is again the default)\n", "\n", "Once the model is created, the parameters can be estimated via maximum likelihood; this is done using the `fit()` method.\n", "\n", "**Note**: recall that we have demeaned and standardized the data; this will be important in interpreting the results that follow.\n", "\n", "**Aside**: in their empirical example, Kim and Nelson (1999) actually consider a slightly different model in which the employment variable is allowed to also depend on lagged values of the factor - this model does not fit into the built-in `DynamicFactor` class, but can be accommodated by using a subclass to implement the required new parameters and restrictions - see Appendix A, below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Parameter estimation\n", "\n", "Multivariate models can have a relatively large number of parameters, and it may be difficult to escape from local minima to find the maximized likelihood. In an attempt to mitigate this problem, I perform an initial maximization step (from the model-defined starting parameters) using the modified Powell method available in Scipy (see the minimize documentation for more information). The resulting parameters are then used as starting parameters in the standard LBFGS optimization method." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:45:40.420744Z", "iopub.status.busy": "2023-12-14T14:45:40.418827Z", "iopub.status.idle": "2023-12-14T14:47:56.140911Z", "shell.execute_reply": "2023-12-14T14:47:56.140173Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n", " warnings.warn(\"Maximum Likelihood optimization failed to \"\n" ] } ], "source": [ "# Get the endogenous data\n", "endog = dta.loc['1979-02-01':, 'std_indprod':'std_emp']\n", "\n", "# Create the model\n", "mod = sm.tsa.DynamicFactor(endog, k_factors=1, factor_order=2, error_order=2)\n", "initial_res = mod.fit(method='powell', disp=False)\n", "res = mod.fit(initial_res.params, disp=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimates\n", "\n", "Once the model has been estimated, there are two components that we can use for analysis or inference:\n", "\n", "- The estimated parameters\n", "- The estimated factor" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Parameters\n", "\n", "The estimated parameters can be helpful in understanding the implications of the model, although in models with a larger number of observed variables and / or unobserved factors they can be difficult to interpret.\n", "\n", "One reason for this difficulty is due to identification issues between the factor loadings and the unobserved factors. One easy-to-see identification issue is the sign of the loadings and the factors: an equivalent model to the one displayed below would result from reversing the signs of all factor loadings and the unobserved factor.\n", "\n", "Here, one of the easy-to-interpret implications in this model is the persistence of the unobserved factor: we find that exhibits substantial persistence." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:47:56.144757Z", "iopub.status.busy": "2023-12-14T14:47:56.144250Z", "iopub.status.idle": "2023-12-14T14:47:56.190899Z", "shell.execute_reply": "2023-12-14T14:47:56.190178Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Statespace Model Results \n", "=================================================================================================================\n", "Dep. Variable: ['std_indprod', 'std_income', 'std_sales', 'std_emp'] No. Observations: 431\n", "Model: DynamicFactor(factors=1, order=2) Log Likelihood -1498.539\n", " + AR(2) errors AIC 3033.079\n", "Date: Thu, 14 Dec 2023 BIC 3106.269\n", "Time: 14:47:56 HQIC 3061.976\n", "Sample: 02-01-1979 \n", " - 12-01-2014 \n", "Covariance Type: opg \n", "====================================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "----------------------------------------------------------------------------------------------------\n", "loading.f1.std_indprod -1.0492 0.030 -34.989 0.000 -1.108 -0.990\n", "loading.f1.std_income -0.3072 0.050 -6.127 0.000 -0.405 -0.209\n", "loading.f1.std_sales -0.5474 0.023 -23.737 0.000 -0.593 -0.502\n", "loading.f1.std_emp -0.2905 0.036 -7.993 0.000 -0.362 -0.219\n", "sigma2.std_indprod 4.213e-07 6.54e-06 0.064 0.949 -1.24e-05 1.32e-05\n", "sigma2.std_income 0.8762 0.027 32.404 0.000 0.823 0.929\n", "sigma2.std_sales 0.5732 0.033 17.627 0.000 0.510 0.637\n", "sigma2.std_emp 0.3715 0.014 25.635 0.000 0.343 0.400\n", "L1.f1.f1 0.2523 0.046 5.439 0.000 0.161 0.343\n", "L2.f1.f1 0.2639 0.053 4.966 0.000 0.160 0.368\n", "L1.e(std_indprod).e(std_indprod) -1.117e-07 2.18e-07 -0.511 0.609 -5.4e-07 3.17e-07\n", "L2.e(std_indprod).e(std_indprod) 1.0000 5.96e-07 1.68e+06 0.000 1.000 1.000\n", "L1.e(std_income).e(std_income) -0.1992 0.021 -9.584 0.000 -0.240 -0.159\n", "L2.e(std_income).e(std_income) -0.1025 0.044 -2.344 0.019 -0.188 -0.017\n", "L1.e(std_sales).e(std_sales) -0.9725 0.041 -23.894 0.000 -1.052 -0.893\n", "L2.e(std_sales).e(std_sales) -0.1919 0.038 -4.993 0.000 -0.267 -0.117\n", "L1.e(std_emp).e(std_emp) 0.3218 0.035 9.282 0.000 0.254 0.390\n", "L2.e(std_emp).e(std_emp) 0.4607 0.028 16.636 0.000 0.406 0.515\n", "=======================================================================================================\n", "Ljung-Box (L1) (Q): 10.19, 0.00, 5.44, 1.85 Jarque-Bera (JB): 2978037.16, 10239.27, 1.30, 73.18\n", "Prob(Q): 0.00, 1.00, 0.02, 0.17 Prob(JB): 0.00, 0.00, 0.52, 0.00\n", "Heteroskedasticity (H): 0.00, 4.00, 0.67, 1.04 Skew: 20.00, -1.12, 0.06, -0.24\n", "Prob(H) (two-sided): 0.00, 0.00, 0.02, 0.81 Kurtosis: 408.25, 26.77, 3.24, 4.96\n", "=======================================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n" ] } ], "source": [ "print(res.summary(separate_params=False))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Estimated factors\n", "\n", "While it can be useful to plot the unobserved factors, it is less useful here than one might think for two reasons:\n", "\n", "1. The sign-related identification issue described above.\n", "2. Since the data was differenced, the estimated factor explains the variation in the differenced data, not the original data.\n", "\n", "It is for these reasons that the coincident index is created (see below).\n", "\n", "With these reservations, the unobserved factor is plotted below, along with the NBER indicators for US recessions. It appears that the factor is successful at picking up some degree of business cycle activity." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:47:56.194422Z", "iopub.status.busy": "2023-12-14T14:47:56.193881Z", "iopub.status.idle": "2023-12-14T14:47:57.096373Z", "shell.execute_reply": "2023-12-14T14:47:57.095686Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(13,3))\n", "\n", "# Plot the factor\n", "dates = endog.index._mpl_repr()\n", "ax.plot(dates, res.factors.filtered[0], label='Factor')\n", "ax.legend()\n", "\n", "# Retrieve and also plot the NBER recession indicators\n", "rec = DataReader('USREC', 'fred', start=start, end=end)\n", "ylim = ax.get_ylim()\n", "ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Post-estimation\n", "\n", "Although here we will be able to interpret the results of the model by constructing the coincident index, there is a useful and generic approach for getting a sense for what is being captured by the estimated factor. By taking the estimated factors as given, regressing them (and a constant) each (one at a time) on each of the observed variables, and recording the coefficients of determination ($R^2$ values), we can get a sense of the variables for which each factor explains a substantial portion of the variance and the variables for which it does not.\n", "\n", "In models with more variables and more factors, this can sometimes lend interpretation to the factors (for example sometimes one factor will load primarily on real variables and another on nominal variables).\n", "\n", "In this model, with only four endogenous variables and one factor, it is easy to digest a simple table of the $R^2$ values, but in larger models it is not. For this reason, a bar plot is often employed; from the plot we can easily see that the factor explains most of the variation in industrial production index and a large portion of the variation in sales and employment, it is less helpful in explaining income." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:47:57.100182Z", "iopub.status.busy": "2023-12-14T14:47:57.099733Z", "iopub.status.idle": "2023-12-14T14:47:57.518619Z", "shell.execute_reply": "2023-12-14T14:47:57.517853Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "res.plot_coefficients_of_determination(figsize=(8,2));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Coincident Index\n", "\n", "As described above, the goal of this model was to create an interpretable series which could be used to understand the current status of the macroeconomy. This is what the coincident index is designed to do. It is constructed below. For readers interested in an explanation of the construction, see Kim and Nelson (1999) or Stock and Watson (1991).\n", "\n", "In essence, what is done is to reconstruct the mean of the (differenced) factor. We will compare it to the coincident index on published by the Federal Reserve Bank of Philadelphia (USPHCI on FRED)." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:47:57.522214Z", "iopub.status.busy": "2023-12-14T14:47:57.521754Z", "iopub.status.idle": "2023-12-14T14:47:58.108230Z", "shell.execute_reply": "2023-12-14T14:47:58.107561Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "usphci = DataReader('USPHCI', 'fred', start='1979-01-01', end='2014-12-01')['USPHCI']\n", "usphci.plot(figsize=(13,3));" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:47:58.112775Z", "iopub.status.busy": "2023-12-14T14:47:58.111646Z", "iopub.status.idle": "2023-12-14T14:47:58.121704Z", "shell.execute_reply": "2023-12-14T14:47:58.121090Z" } }, "outputs": [], "source": [ "dusphci = usphci.diff()[1:].values\n", "def compute_coincident_index(mod, res):\n", " # Estimate W(1)\n", " spec = res.specification\n", " design = mod.ssm['design']\n", " transition = mod.ssm['transition']\n", " ss_kalman_gain = res.filter_results.kalman_gain[:,:,-1]\n", " k_states = ss_kalman_gain.shape[0]\n", "\n", " W1 = np.linalg.inv(np.eye(k_states) - np.dot(\n", " np.eye(k_states) - np.dot(ss_kalman_gain, design),\n", " transition\n", " )).dot(ss_kalman_gain)[0]\n", "\n", " # Compute the factor mean vector\n", " factor_mean = np.dot(W1, dta.loc['1972-02-01':, 'dln_indprod':'dln_emp'].mean())\n", " \n", " # Normalize the factors\n", " factor = res.factors.filtered[0]\n", " factor *= np.std(usphci.diff()[1:]) / np.std(factor)\n", "\n", " # Compute the coincident index\n", " coincident_index = np.zeros(mod.nobs+1)\n", " # The initial value is arbitrary; here it is set to\n", " # facilitate comparison\n", " coincident_index[0] = usphci.iloc[0] * factor_mean / dusphci.mean()\n", " for t in range(0, mod.nobs):\n", " coincident_index[t+1] = coincident_index[t] + factor[t] + factor_mean\n", " \n", " # Attach dates\n", " coincident_index = pd.Series(coincident_index, index=dta.index).iloc[1:]\n", " \n", " # Normalize to use the same base year as USPHCI\n", " coincident_index *= (usphci.loc['1992-07-01'] / coincident_index.loc['1992-07-01'])\n", " \n", " return coincident_index" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we plot the calculated coincident index along with the US recessions and the comparison coincident index USPHCI." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:47:58.126223Z", "iopub.status.busy": "2023-12-14T14:47:58.125074Z", "iopub.status.idle": "2023-12-14T14:47:58.464764Z", "shell.execute_reply": "2023-12-14T14:47:58.464094Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(13,3))\n", "\n", "# Compute the index\n", "coincident_index = compute_coincident_index(mod, res)\n", "\n", "# Plot the factor\n", "dates = endog.index._mpl_repr()\n", "ax.plot(dates, coincident_index, label='Coincident index')\n", "ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')\n", "ax.legend(loc='lower right')\n", "\n", "# Retrieve and also plot the NBER recession indicators\n", "ylim = ax.get_ylim()\n", "ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Appendix 1: Extending the dynamic factor model\n", "\n", "Recall that the previous specification was described by:\n", "\n", "$$\n", "\\begin{align}\n", "y_{i,t} & = \\lambda_i f_t + u_{i,t} \\\\\n", "u_{i,t} & = c_{i,1} u_{1,t-1} + c_{i,2} u_{i,t-2} + \\varepsilon_{i,t} \\qquad & \\varepsilon_{i,t} \\sim N(0, \\sigma_i^2) \\\\\n", "f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \\eta_t \\qquad & \\eta_t \\sim N(0, I)\\\\\n", "\\end{align}\n", "$$\n", "\n", "Written in state space form, the previous specification of the model had the following observation equation:\n", "\n", "$$\n", "\\begin{bmatrix}\n", "y_{\\text{indprod}, t} \\\\\n", "y_{\\text{income}, t} \\\\\n", "y_{\\text{sales}, t} \\\\\n", "y_{\\text{emp}, t} \\\\\n", "\\end{bmatrix} = \\begin{bmatrix}\n", "\\lambda_\\text{indprod} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "\\lambda_\\text{income} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "\\lambda_\\text{sales} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n", "\\lambda_\\text{emp} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n", "\\end{bmatrix}\n", "\\begin{bmatrix}\n", "f_t \\\\\n", "f_{t-1} \\\\\n", "u_{\\text{indprod}, t} \\\\\n", "u_{\\text{income}, t} \\\\\n", "u_{\\text{sales}, t} \\\\\n", "u_{\\text{emp}, t} \\\\\n", "u_{\\text{indprod}, t-1} \\\\\n", "u_{\\text{income}, t-1} \\\\\n", "u_{\\text{sales}, t-1} \\\\\n", "u_{\\text{emp}, t-1} \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "and transition equation:\n", "\n", "$$\n", "\\begin{bmatrix}\n", "f_t \\\\\n", "f_{t-1} \\\\\n", "u_{\\text{indprod}, t} \\\\\n", "u_{\\text{income}, t} \\\\\n", "u_{\\text{sales}, t} \\\\\n", "u_{\\text{emp}, t} \\\\\n", "u_{\\text{indprod}, t-1} \\\\\n", "u_{\\text{income}, t-1} \\\\\n", "u_{\\text{sales}, t-1} \\\\\n", "u_{\\text{emp}, t-1} \\\\\n", "\\end{bmatrix} = \\begin{bmatrix}\n", "a_1 & a_2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & c_{\\text{indprod}, 1} & 0 & 0 & 0 & c_{\\text{indprod}, 2} & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & c_{\\text{income}, 1} & 0 & 0 & 0 & c_{\\text{income}, 2} & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & c_{\\text{sales}, 1} & 0 & 0 & 0 & c_{\\text{sales}, 2} & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & c_{\\text{emp}, 1} & 0 & 0 & 0 & c_{\\text{emp}, 2} \\\\\n", "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n", "\\end{bmatrix} \n", "\\begin{bmatrix}\n", "f_{t-1} \\\\\n", "f_{t-2} \\\\\n", "u_{\\text{indprod}, t-1} \\\\\n", "u_{\\text{income}, t-1} \\\\\n", "u_{\\text{sales}, t-1} \\\\\n", "u_{\\text{emp}, t-1} \\\\\n", "u_{\\text{indprod}, t-2} \\\\\n", "u_{\\text{income}, t-2} \\\\\n", "u_{\\text{sales}, t-2} \\\\\n", "u_{\\text{emp}, t-2} \\\\\n", "\\end{bmatrix}\n", "+ R \\begin{bmatrix}\n", "\\eta_t \\\\\n", "\\varepsilon_{t}\n", "\\end{bmatrix}\n", "$$\n", "\n", "the `DynamicFactor` model handles setting up the state space representation and, in the `DynamicFactor.update` method, it fills in the fitted parameter values into the appropriate locations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The extended specification is the same as in the previous example, except that we also want to allow employment to depend on lagged values of the factor. This creates a change to the $y_{\\text{emp},t}$ equation. Now we have:\n", "\n", "$$\n", "\\begin{align}\n", "y_{i,t} & = \\lambda_i f_t + u_{i,t} \\qquad & i \\in \\{\\text{indprod}, \\text{income}, \\text{sales} \\}\\\\\n", "y_{i,t} & = \\lambda_{i,0} f_t + \\lambda_{i,1} f_{t-1} + \\lambda_{i,2} f_{t-2} + \\lambda_{i,2} f_{t-3} + u_{i,t} \\qquad & i = \\text{emp} \\\\\n", "u_{i,t} & = c_{i,1} u_{i,t-1} + c_{i,2} u_{i,t-2} + \\varepsilon_{i,t} \\qquad & \\varepsilon_{i,t} \\sim N(0, \\sigma_i^2) \\\\\n", "f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \\eta_t \\qquad & \\eta_t \\sim N(0, I)\\\\\n", "\\end{align}\n", "$$\n", "\n", "Now, the corresponding observation equation should look like the following:\n", "\n", "$$\n", "\\begin{bmatrix}\n", "y_{\\text{indprod}, t} \\\\\n", "y_{\\text{income}, t} \\\\\n", "y_{\\text{sales}, t} \\\\\n", "y_{\\text{emp}, t} \\\\\n", "\\end{bmatrix} = \\begin{bmatrix}\n", "\\lambda_\\text{indprod} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "\\lambda_\\text{income} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "\\lambda_\\text{sales} & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n", "\\lambda_\\text{emp,1} & \\lambda_\\text{emp,2} & \\lambda_\\text{emp,3} & \\lambda_\\text{emp,4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n", "\\end{bmatrix}\n", "\\begin{bmatrix}\n", "f_t \\\\\n", "f_{t-1} \\\\\n", "f_{t-2} \\\\\n", "f_{t-3} \\\\\n", "u_{\\text{indprod}, t} \\\\\n", "u_{\\text{income}, t} \\\\\n", "u_{\\text{sales}, t} \\\\\n", "u_{\\text{emp}, t} \\\\\n", "u_{\\text{indprod}, t-1} \\\\\n", "u_{\\text{income}, t-1} \\\\\n", "u_{\\text{sales}, t-1} \\\\\n", "u_{\\text{emp}, t-1} \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "Notice that we have introduced two new state variables, $f_{t-2}$ and $f_{t-3}$, which means we need to update the transition equation:\n", "\n", "$$\n", "\\begin{bmatrix}\n", "f_t \\\\\n", "f_{t-1} \\\\\n", "f_{t-2} \\\\\n", "f_{t-3} \\\\\n", "u_{\\text{indprod}, t} \\\\\n", "u_{\\text{income}, t} \\\\\n", "u_{\\text{sales}, t} \\\\\n", "u_{\\text{emp}, t} \\\\\n", "u_{\\text{indprod}, t-1} \\\\\n", "u_{\\text{income}, t-1} \\\\\n", "u_{\\text{sales}, t-1} \\\\\n", "u_{\\text{emp}, t-1} \\\\\n", "\\end{bmatrix} = \\begin{bmatrix}\n", "a_1 & a_2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & c_{\\text{indprod}, 1} & 0 & 0 & 0 & c_{\\text{indprod}, 2} & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & c_{\\text{income}, 1} & 0 & 0 & 0 & c_{\\text{income}, 2} & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & c_{\\text{sales}, 1} & 0 & 0 & 0 & c_{\\text{sales}, 2} & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & 0 & c_{\\text{emp}, 1} & 0 & 0 & 0 & c_{\\text{emp}, 2} \\\\\n", "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n", "\\end{bmatrix} \n", "\\begin{bmatrix}\n", "f_{t-1} \\\\\n", "f_{t-2} \\\\\n", "f_{t-3} \\\\\n", "f_{t-4} \\\\\n", "u_{\\text{indprod}, t-1} \\\\\n", "u_{\\text{income}, t-1} \\\\\n", "u_{\\text{sales}, t-1} \\\\\n", "u_{\\text{emp}, t-1} \\\\\n", "u_{\\text{indprod}, t-2} \\\\\n", "u_{\\text{income}, t-2} \\\\\n", "u_{\\text{sales}, t-2} \\\\\n", "u_{\\text{emp}, t-2} \\\\\n", "\\end{bmatrix}\n", "+ R \\begin{bmatrix}\n", "\\eta_t \\\\\n", "\\varepsilon_{t}\n", "\\end{bmatrix}\n", "$$\n", "\n", "This model cannot be handled out-of-the-box by the `DynamicFactor` class, but it can be handled by creating a subclass when alters the state space representation in the appropriate way." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, notice that if we had set `factor_order = 4`, we would almost have what we wanted. In that case, the last line of the observation equation would be:\n", "\n", "$$\n", "\\begin{bmatrix}\n", "\\vdots \\\\\n", "y_{\\text{emp}, t} \\\\\n", "\\end{bmatrix} = \\begin{bmatrix}\n", "\\vdots & & & & & & & & & & & \\vdots \\\\\n", "\\lambda_\\text{emp,1} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n", "\\end{bmatrix}\n", "\\begin{bmatrix}\n", "f_t \\\\\n", "f_{t-1} \\\\\n", "f_{t-2} \\\\\n", "f_{t-3} \\\\\n", "\\vdots\n", "\\end{bmatrix}\n", "$$\n", "\n", "\n", "and the first line of the transition equation would be:\n", "\n", "$$\n", "\\begin{bmatrix}\n", "f_t \\\\\n", "\\vdots\n", "\\end{bmatrix} = \\begin{bmatrix}\n", "a_1 & a_2 & a_3 & a_4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "\\vdots & & & & & & & & & & & \\vdots \\\\\n", "\\end{bmatrix} \n", "\\begin{bmatrix}\n", "f_{t-1} \\\\\n", "f_{t-2} \\\\\n", "f_{t-3} \\\\\n", "f_{t-4} \\\\\n", "\\vdots\n", "\\end{bmatrix}\n", "+ R \\begin{bmatrix}\n", "\\eta_t \\\\\n", "\\varepsilon_{t}\n", "\\end{bmatrix}\n", "$$\n", "\n", "Relative to what we want, we have the following differences:\n", "\n", "1. In the above situation, the $\\lambda_{\\text{emp}, j}$ are forced to be zero for $j > 0$, and we want them to be estimated as parameters.\n", "2. We only want the factor to transition according to an AR(2), but under the above situation it is an AR(4).\n", "\n", "Our strategy will be to subclass `DynamicFactor`, and let it do most of the work (setting up the state space representation, etc.) where it assumes that `factor_order = 4`. The only things we will actually do in the subclass will be to fix those two issues.\n", "\n", "First, here is the full code of the subclass; it is discussed below. It is important to note at the outset that none of the methods defined below could have been omitted. In fact, the methods `__init__`, `start_params`, `param_names`, `transform_params`, `untransform_params`, and `update` form the core of all state space models in statsmodels, not just the `DynamicFactor` class." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:47:58.470658Z", "iopub.status.busy": "2023-12-14T14:47:58.468960Z", "iopub.status.idle": "2023-12-14T14:47:58.493403Z", "shell.execute_reply": "2023-12-14T14:47:58.492758Z" } }, "outputs": [], "source": [ "from statsmodels.tsa.statespace import tools\n", "class ExtendedDFM(sm.tsa.DynamicFactor):\n", " def __init__(self, endog, **kwargs):\n", " # Setup the model as if we had a factor order of 4\n", " super(ExtendedDFM, self).__init__(\n", " endog, k_factors=1, factor_order=4, error_order=2,\n", " **kwargs)\n", "\n", " # Note: `self.parameters` is an ordered dict with the\n", " # keys corresponding to parameter types, and the values\n", " # the number of parameters of that type.\n", " # Add the new parameters\n", " self.parameters['new_loadings'] = 3\n", "\n", " # Cache a slice for the location of the 4 factor AR\n", " # parameters (a_1, ..., a_4) in the full parameter vector\n", " offset = (self.parameters['factor_loadings'] +\n", " self.parameters['exog'] +\n", " self.parameters['error_cov'])\n", " self._params_factor_ar = np.s_[offset:offset+2]\n", " self._params_factor_zero = np.s_[offset+2:offset+4]\n", "\n", " @property\n", " def start_params(self):\n", " # Add three new loading parameters to the end of the parameter\n", " # vector, initialized to zeros (for simplicity; they could\n", " # be initialized any way you like)\n", " return np.r_[super(ExtendedDFM, self).start_params, 0, 0, 0]\n", " \n", " @property\n", " def param_names(self):\n", " # Add the corresponding names for the new loading parameters\n", " # (the name can be anything you like)\n", " return super(ExtendedDFM, self).param_names + [\n", " 'loading.L%d.f1.%s' % (i, self.endog_names[3]) for i in range(1,4)]\n", "\n", " def transform_params(self, unconstrained):\n", " # Perform the typical DFM transformation (w/o the new parameters)\n", " constrained = super(ExtendedDFM, self).transform_params(\n", " unconstrained[:-3])\n", "\n", " # Redo the factor AR constraint, since we only want an AR(2),\n", " # and the previous constraint was for an AR(4)\n", " ar_params = unconstrained[self._params_factor_ar]\n", " constrained[self._params_factor_ar] = (\n", " tools.constrain_stationary_univariate(ar_params))\n", "\n", " # Return all the parameters\n", " return np.r_[constrained, unconstrained[-3:]]\n", "\n", " def untransform_params(self, constrained):\n", " # Perform the typical DFM untransformation (w/o the new parameters)\n", " unconstrained = super(ExtendedDFM, self).untransform_params(\n", " constrained[:-3])\n", "\n", " # Redo the factor AR unconstrained, since we only want an AR(2),\n", " # and the previous unconstrained was for an AR(4)\n", " ar_params = constrained[self._params_factor_ar]\n", " unconstrained[self._params_factor_ar] = (\n", " tools.unconstrain_stationary_univariate(ar_params))\n", "\n", " # Return all the parameters\n", " return np.r_[unconstrained, constrained[-3:]]\n", "\n", " def update(self, params, transformed=True, **kwargs):\n", " # Peform the transformation, if required\n", " if not transformed:\n", " params = self.transform_params(params)\n", " params[self._params_factor_zero] = 0\n", " \n", " # Now perform the usual DFM update, but exclude our new parameters\n", " super(ExtendedDFM, self).update(params[:-3], transformed=True, **kwargs)\n", "\n", " # Finally, set our new parameters in the design matrix\n", " self.ssm['design', 3, 1:4] = params[-3:]\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So what did we just do?\n", "\n", "**`__init__`**\n", "\n", "The important step here was specifying the base dynamic factor model which we were operating with. In particular, as described above, we initialize with `factor_order=4`, even though we will only end up with an AR(2) model for the factor. We also performed some general setup-related tasks.\n", "\n", "**`start_params`**\n", "\n", "`start_params` are used as initial values in the optimizer. Since we are adding three new parameters, we need to pass those in. If we had not done this, the optimizer would use the default starting values, which would be three elements short.\n", "\n", "**`param_names`**\n", "\n", "`param_names` are used in a variety of places, but especially in the results class. Below we get a full result summary, which is only possible when all the parameters have associated names.\n", "\n", "**`transform_params`** and **`untransform_params`**\n", "\n", "The optimizer selects possibly parameter values in an unconstrained way. That's not usually desired (since variances cannot be negative, for example), and `transform_params` is used to transform the unconstrained values used by the optimizer to constrained values appropriate to the model. Variances terms are typically squared (to force them to be positive), and AR lag coefficients are often constrained to lead to a stationary model. `untransform_params` is used for the reverse operation (and is important because starting parameters are usually specified in terms of values appropriate to the model, and we need to convert them to parameters appropriate to the optimizer before we can begin the optimization routine).\n", "\n", "Even though we do not need to transform or untransform our new parameters (the loadings can in theory take on any values), we still need to modify this function for two reasons:\n", "\n", "1. The version in the `DynamicFactor` class is expecting 3 fewer parameters than we have now. At a minimum, we need to handle the three new parameters.\n", "2. The version in the `DynamicFactor` class constrains the factor lag coefficients to be stationary as though it was an AR(4) model. Since we actually have an AR(2) model, we need to re-do the constraint. We also set the last two autoregressive coefficients to be zero here.\n", "\n", "**`update`**\n", "\n", "The most important reason we need to specify a new `update` method is because we have three new parameters that we need to place into the state space formulation. In particular we let the parent `DynamicFactor.update` class handle placing all the parameters except the three new ones in to the state space representation, and then we put the last three in manually." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:47:58.498944Z", "iopub.status.busy": "2023-12-14T14:47:58.497316Z", "iopub.status.idle": "2023-12-14T14:48:09.576178Z", "shell.execute_reply": "2023-12-14T14:48:09.575489Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 4.731939\n", " Iterations: 715\n", " Function evaluations: 1142\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Statespace Model Results \n", "=================================================================================================================\n", "Dep. Variable: ['std_indprod', 'std_income', 'std_sales', 'std_emp'] No. Observations: 431\n", "Model: DynamicFactor(factors=1, order=4) Log Likelihood -2039.466\n", " + AR(2) errors AIC 4124.932\n", "Date: Thu, 14 Dec 2023 BIC 4218.452\n", "Time: 14:48:09 HQIC 4161.857\n", "Sample: 02-01-1979 \n", " - 12-01-2014 \n", "Covariance Type: opg \n", "====================================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "----------------------------------------------------------------------------------------------------\n", "loading.f1.std_indprod -0.9067 0.021 -44.062 0.000 -0.947 -0.866\n", "loading.f1.std_income -0.2494 0.045 -5.589 0.000 -0.337 -0.162\n", "loading.f1.std_sales -0.5049 0.026 -19.087 0.000 -0.557 -0.453\n", "loading.f1.std_emp -0.3235 0.030 -10.658 0.000 -0.383 -0.264\n", "sigma2.std_indprod 3.477e-12 0.005 6.45e-10 1.000 -0.011 0.011\n", "sigma2.std_income 0.9052 0.029 30.762 0.000 0.848 0.963\n", "sigma2.std_sales 0.5894 0.034 17.265 0.000 0.523 0.656\n", "sigma2.std_emp 0.3441 0.014 24.736 0.000 0.317 0.371\n", "L1.f1.f1 0.2274 0.041 5.596 0.000 0.148 0.307\n", "L2.f1.f1 0.2861 0.047 6.090 0.000 0.194 0.378\n", "L3.f1.f1 0 2.75e-12 0 1.000 -5.39e-12 5.39e-12\n", "L4.f1.f1 0 2.75e-12 0 1.000 -5.39e-12 5.39e-12\n", "L1.e(std_indprod).e(std_indprod) -0.3277 7.61e-11 -4.3e+09 0.000 -0.328 -0.328\n", "L2.e(std_indprod).e(std_indprod) 0.5782 4.76e-11 1.21e+10 0.000 0.578 0.578\n", "L1.e(std_income).e(std_income) -0.1848 0.022 -8.416 0.000 -0.228 -0.142\n", "L2.e(std_income).e(std_income) -0.0896 0.047 -1.899 0.058 -0.182 0.003\n", "L1.e(std_sales).e(std_sales) -0.4270 0.043 -9.964 0.000 -0.511 -0.343\n", "L2.e(std_sales).e(std_sales) -0.1947 0.049 -3.941 0.000 -0.292 -0.098\n", "L1.e(std_emp).e(std_emp) 0.2392 0.034 7.000 0.000 0.172 0.306\n", "L2.e(std_emp).e(std_emp) 0.4488 0.035 13.006 0.000 0.381 0.516\n", "loading.L1.f1.std_emp -0.1246 0.031 -3.990 0.000 -0.186 -0.063\n", "loading.L2.f1.std_emp -0.1061 0.028 -3.755 0.000 -0.161 -0.051\n", "loading.L3.f1.std_emp -0.1190 0.030 -3.998 0.000 -0.177 -0.061\n", "====================================================================================================\n", "Ljung-Box (L1) (Q): 0.43, 0.03, 0.04, 6.29 Jarque-Bera (JB): 250.38, 9954.42, 20.23, 4653.64\n", "Prob(Q): 0.51, 0.85, 0.84, 0.01 Prob(JB): 0.00, 0.00, 0.00, 0.00\n", "Heteroskedasticity (H): 0.77, 4.66, 0.47, 0.38 Skew: 0.13, -1.00, 0.21, 0.81\n", "Prob(H) (two-sided): 0.11, 0.00, 0.00, 0.00 Kurtosis: 6.72, 26.46, 3.97, 19.02\n", "====================================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n", "[2] Covariance matrix is singular or near-singular, with condition number 1.17e+18. Standard errors may be unstable.\n" ] } ], "source": [ "# Create the model\n", "extended_mod = ExtendedDFM(endog)\n", "initial_extended_res = extended_mod.fit(maxiter=1000, disp=False)\n", "extended_res = extended_mod.fit(initial_extended_res.params, method='nm', maxiter=1000)\n", "print(extended_res.summary(separate_params=False))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although this model increases the likelihood, it is not preferred by the AIC and BIC measures which penalize the additional three parameters.\n", "\n", "Furthermore, the qualitative results are unchanged, as we can see from the updated $R^2$ chart and the new coincident index, both of which are practically identical to the previous results." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:48:09.580058Z", "iopub.status.busy": "2023-12-14T14:48:09.579675Z", "iopub.status.idle": "2023-12-14T14:48:09.817259Z", "shell.execute_reply": "2023-12-14T14:48:09.816491Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "extended_res.plot_coefficients_of_determination(figsize=(8,2));" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:48:09.820691Z", "iopub.status.busy": "2023-12-14T14:48:09.820377Z", "iopub.status.idle": "2023-12-14T14:48:10.345709Z", "shell.execute_reply": "2023-12-14T14:48:10.344778Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(13,3))\n", "\n", "# Compute the index\n", "extended_coincident_index = compute_coincident_index(extended_mod, extended_res)\n", "\n", "# Plot the factor\n", "dates = endog.index._mpl_repr()\n", "ax.plot(dates, coincident_index, '-', linewidth=1, label='Basic model')\n", "ax.plot(dates, extended_coincident_index, '--', linewidth=3, label='Extended model')\n", "ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')\n", "ax.legend(loc='lower right')\n", "ax.set(title='Coincident indices, comparison')\n", "\n", "# Retrieve and also plot the NBER recession indicators\n", "ylim = ax.get_ylim()\n", "ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1);" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 4 }