# Approaching a time series before building a predictive model

I have a big task at hand - building a predictive model that predicts the amount of fires in a certain region of a certain city tomorrow based on historical data. Currently the problem was narrowed down to constructing a time series of amount of fires per date and inspecting it. What should I do to the time series to pick the right predictive algorithm? I have done an autocorrelation check which showed little to no autocorrelation.

My question is purely about approaching the problem. What actions should one take first when inspecting a time series?

If you want to do time series prediction and you have a sample of a univariate time series at hand, you would start by plotting it and familiarizing yourself with it. Then you would try to find patterns with the hope of extrapolating them into the future1. There could be, for example,

• seasonality -- in conditional mean or variance (or even higher-order moments);
• autocorrelation;
• autoregressive conditional heteroskedasticity.

To discover these patterns, you could use

• seasonal plots (slice the time series into full periods, e.g. years, and plot those on top of each other); function seasonplot in "forecast" package in R;
• (partial) autocorrelation plots (ACF and PACF); functions acf and pacf in R;
• (partial) autocorrelation plots (ACF and PACF) on squared mean-adjusted data.

Once you have identified some patterns, you could then start developing models.

1Beware of outliers and nonstationary behaviour, e.g. long-lasting changes in level or variance of the series. When neglected, they could seriously affect your diagnostics of seasonality, autocorrelation and autoregressive conditional heteroskedasticity. Outliers and nonstationarities should be dealt with first.

I'm not an expert here, but I suggest some simple first steps: 1. do some explorative analysis by plotting the data 2. use some simple standard models, evaluate them (by plotting or cross-validation) and see which works for you