Time Series Models

Time series analysis and forecasting have many applications, because of its “claimed” capability in predicting the future. This blog covers some of the most classic statistical time series models. It is intended to remind myself of some important concepts. Therefore, apologize for any unclearness.

The essential goal of time series model is to extract all the information from the data, so that the only left in the data is just white noise. Such a white noise series is called Stationary, whose property do not depend on time.

Since real-world time series can have high-order dependency, models in this blog refers to stationary as zero mean and constant variance.

If a time series has auto-correlation, which is correlation with its lags, it is not stationary.

Autoregressive Models AR(p)

Moving Average Model ma(q), based on previous errors made from using averages.

ARMA(p,q)

ARIMA(p,d,q)

SARIMA(p,d,q) * (P,D,Q)_s

ARIMAX

ARCH

GARCH

Besides above models, Bayesian methods, Machine Learning, and Deep Learning, etc have their own approaches to time series forecasting, and shown superior performance. I may write later blogs to write related topics.

Thanks for reading, and hope you find it useful!