Time Series part I: White Noise and Random Walk Models

Time series data can be very useful when it comes to prices, stocks, and anything that has to do with time/date. What we are looking for in Time Series models is patterns over time so we can predict what will happen in the future. The first two basic models are White Noise and Random Walk Models.

White Noise

When we look at a White Noise model as a plot it is a plot without a trend. There are 3 main properties of a White Noise Model.

• Fixed and constant mean
• Fixed and constant variance
• No correlation over time

Usually the stock market is considered a White Noise model.

Random Walk

A Random Walk model has 2 important properties

• No specific mean or variance
• Strong dependence over time

Finance are usually Random Walk models. What happened that day may influence what is going to happen tomorrow.

Correlation, Autocorrelation, Partial Autocorrelation

Correlation is a statistical technique that specifies how strongly pairs of variables rely on each other. There can be correlation in Time Series models, think about traffic, at certain times of the day there are always more traffic than other times. Autocorrelation is a strong technique to determine how related our current observation is related to its past. You can find the autocorrelation by performing the Autocorrelation Function (ACF). What this function does is give you a summary of each lag performed on the model. On the other hand we also have the Partial Autocorrelation Function (PACF). The PACF gives the partial correlation of its own lags.