The role of exogenous and lagged variables in ARIMA and linear regression models

The comparison of an autoregressive model with exogenous regressors and the linear regression model is a recurrent question at Cross Validated. The question often arises when an autoregressive model with exogenous variables is fitted as a linear regression model with … Continue reading

Posted in time series | Tagged , , , | Leave a comment

Signal extraction in time series, as simple as that?

Frequency-domain filters provide a straightforward way to decompose a time series. In this post I briefly introduce this approach advocated by Prof. D. Stephen G. Pollock in this document that introduces the software IDEOLOG. As pointed out by Prof. Pollock, … Continue reading

Posted in R, time series | Tagged , , , | Leave a comment

Testing for seasonal stability
Canova and Hansen test statistic

Seasonal patterns are common in many time series data (e.g. macroeconomic or meteorological data). One of the issues to be analyzed when working with seasonal data is whether the seasonal pattern remains relatively stable over the sample period or whether … Continue reading

Posted in R, time series | Tagged , , | Leave a comment

Does a seasonal ARIMA model involve seasonality?

The question posed in the title may seem a tautology, but it’s not. If an ARIMA model (chosen by any manual or automated procedure) contains lags of seasonal order, it does not necessarily mean that there is a relevant seasonal … Continue reading

Posted in time series | Tagged , | Leave a comment

$$F$$-test statistic in autoregressive models

Under the framework of the classical linear regression model, the ordinary least squares (OLS) estimator has good properties: it is unbiased, has minimum variance compared to other linear estimators and the usual test statistics follow common distributions. An autoregressive model … Continue reading

Posted in regression model, simulations, time series | Tagged , , | Leave a comment