Time Series part II: ARMA Models

Autoregressive

An autoregressive model is when a value is regressed over previous values from the same model. In other words an autoregressive model makes predictions based on past behavior.

today = constant+slope*yesterday+noise

• if the slope is 0 we are working with a white noise model(Fixed and constant mean, fixed and constant variance, no correlation over time)
• if the slope is not 0 the series is autocorrelated
• larger slope = higher autocorrelated
• negative slope =oscillatory process(goes high-low high-low)

Moving Average Model

Moving average model is just what it sounds like. It is an adjustable average that is the weighted sum of today’s noise and yesterday’s noise.

today=mean+noise+slope*yesterday’s noise

• slope = 0, the time series is a white noise model with mean mu
• slope is not 0, the time series is autocorrelated and depends on the previous white noise process

ARMA model

Can we combine autoregressive and moving average models? Yes. We. Can. We can use the the past behavior(autoregressive) and combine that with yesterday’s errors (moving average).