Spatial Panel VAR and Application to Forecast Influenza Incidence Rates of US States

Abstract

In this paper, we propose a spatial panel vector autoregression, SPVAR(p), which generalizes the spatial dynamic panel data (SDPD) models with individual fixed effects to allow for multivariate vector observations and higher order lags. The regression residuals can be independently or spatial autoregressively (SAR) distributed. We investigate in the issues of identification and estimation via profile QMLE. We prove that the QML estimators are consistent and asymptotically normally distributed when both N and T are large. Then, we analyze the bias and bias correction. The finite sample performance of the profile QMLE is evaluated by Monte Carlo simulations. Information criteria and likelihood ratio test are used to select the lag orders and test the residual specifications in the SPVAR(p). The SPVAR(p) is then used to estimate and forecast the incidence rates of influenza like illness (ILI) in the United States. We combine weekly ILI incidence rate data by Google Flu Trends and the office of Centers for Disease Control and Prevention (CDC) into a vector measure for 48 US continental states, and then we use the vector observations to estimate the SPVAR(p) model, where the spatial weight matrix is the row normalized state geographical adjacency matrix. We use state population density, temperature, and precipitation as predictors. We find that SPVAR(p) achieves satisfactory in-sample estimates and out-of-sample forecasts based on Google Flu Trends and CDC ILI incidence rate data. The estimated SPVAR(p) is compared against univariate SDPD(p) model of Google Flu Trends ILI incidence rates. We also conduct an impulse response analysis of the dynamic diffusions of California flu shock.