5.4 Time series models

After our GUI is deployed (see Figure 5.1), the user should select Time Series Models from the top panel. Then, Figure 5.8 will be displayed, and the user will see the radio button on the left-hand side, which shows the specific models within this general class.

Time series models.

Figure 5.8: Time series models.

Users can perform inference using dynamic linear models (DLM), autoregressive moving average (ARMA) models, stochastic volatility models (SVM), and vector autoregressive (VAR) models. Users should upload a dataset, which must be a csv file with headers in the first row. The files for DLMs and SVMs have the same structure: the first column contains the dependent variable, followed by the independent variables. For ARMA models, there is only one column with the modeled variable, while VAR models have each modeled variable in a separate column. Note that this version of the GUI does not allow for exogenous variables in VAR models. Users should specify the separator used in the input file: comma, semicolon, or tab. A dataset preview is displayed once the file is uploaded. Dataset templates can be found in the folders DataSim and DataApp (see the Appendix for details) in our GitHub repository.

Next, users should set the MCMC and burn-in iterations using the range sliders and the thinning parameter using the input box.

To estimate DLMs, users should set the hyperparameters for the precision of the observation equation and the state equations (means and variances) if prior information is available. Otherwise, users can click the Pre Calculate Prior button, where these hyperparameters are estimated based on a recursive model estimation using ordinary least squares (OLS). The sample size is progressively increased, and the location parameters are saved. The GUI then computes the covariance matrix of this sequence and uses it to set the prior mean for the precision of the state vector, which is equal to the inverse of the maximum element on the main diagonal of the covariance matrix (a.theta). The prior variance is set to ten times this value (b.theta). For the observation equation, the prior mean of the precision is set to the inverse of the OLS variance estimate (a.y), and the prior variance is set to ten times this value (b.y). This is a rudimentary approach to setting these hyperparameters, and users are encouraged to use a more thoughtful process.

Next, users should click the Go! button to start estimating the model. This may take a few minutes, as DLMs are complex to estimate. Users should be patient. Once the estimation is complete, the GUI will display graphs of the states (mean and 95% credible intervals), summary statistics of the posterior chains for the observation and state variances, and convergence diagnostics. Users can download the mean and the lower and upper limits of the 95% credible intervals of the states, as well as the posterior chains for the variances.

For ARMA models, users need to set the frequency (annual -1-, quarterly -4-, and monthly -12-), as well as the AR and MA orders (see Figure 5.9). Then, users should set the location and scale hyperparameters for the intercept, autoregressive (AR), moving average (MA), and standard deviation terms. Note that there is only one set of hyperparameters for the AR and MA coefficients. This step is optional, as the GUI uses non-informative priors by default.

Time series models: ARMA specification.

Figure 5.9: Time series models: ARMA specification.

Then, users should click the Go! button, and the GUI will start estimating the model. The GUI will display the summary statistics of the posterior draws and the convergence diagnostics. The order is AR coefficients (if any), MA coefficients (if any), intercept, and standard deviation. Users can download the posterior chains and figures (density, autocorrelation, and trace plots).

Estimation of the SVMs requires setting the coefficients of the mean and standard deviation of the Gaussian prior for the regression parameters, the mean and standard deviation for the Gaussian prior distribution of the level of the log-volatility, shape parameters for the Beta prior distribution of the transformed persistence parameter, and a positive real number representing the scaling of the transformed volatility of log-volatility. However, this step is not necessary, as by default our GUI uses the default values in the stochvol package.

Then, click the Go! button, wait for the estimation to be completed, and the GUI will display the stochastic volatility plot (mean and 95% credible interval). Users can also view the summary and diagnostics of the posterior chains (see Figure 5.10). In addition, users can download the mean and the lower and upper limits of the 95% credible intervals of the stochastic volatility, as well as the posterior chains of the variances.

Time series models: Stochastic volatility.

Figure 5.10: Time series models: Stochastic volatility.

To estimate VAR models, users should set the number of lags, the impulse response and forecast periods, the three coefficients of the Minnesota prior, and the type of impulse response (forecast error impulse response -feir- or orthogonalized impulse response -other-, both cumulative or non-cumulative). See Chapter 8 for details, Section 8.4.

Click the Go! button, and after a few minutes, users will be able to see the plots of the impulse responses and forecasts (means and 95% credible intervals). Click the Download Results button, and a zip file with .csv files containing the impulse responses and forecasts, along with their plots, will be downloaded.