# Time Series Modelling

## Abstract

Time series data consist of readings on a variable taken at equally intervals of time. How would one compute the mean of a time series of a specified length? Calculating the mean of a sequence of observations might appear to be a trivial problem, as we would just sum all readings and divide by their number. However, if the series is steadily increasing overtime, i.e. exhibits a trend and we make decisions based on this mean, we would certainly not, for example, want to use this parameter as a forecast of the future level of the series. We would also not use the overall mean to make inferences (e.g. as the centre of confidence intervals) at time periods at the beginning or end the series. If we regard our gathered series as but one example of all possible series that could be generated by the same mechanism, we are further faced with the problem of estimating the mean for each time period, as we have a sample only of one item. It is similarly impossible to estimate the variance at any one time period.

## Reference

- Box, G.E.P., & Pierce, D.A. (1970). Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association, 65, 1509–1526.MathSciNetCrossRefGoogle Scholar