Forecasting with time series analysis

Forecasting is a method that is used extensively in time series analysis to predict a response variable, such as monthly profits, stock performance, or unemployment figures, for a specified period of time. Forecasts are based on patterns in existing data. For example, a warehouse manager can model how much product to order for the next 3 months based on the previous 12 months of orders.

You can use a variety of time series methods, such as trend analysis, decomposition, or single exponential smoothing, to model patterns in the data and extrapolate those patterns to the future. Choose an analysis method by whether the patterns are static (constant over time) or dynamic (change over time), the nature of the trend and seasonal components, and how far ahead you want to forecast. Before producing forecasts, fit several candidate models to the data to determine which model is the most stable and accurate.

In naive forecasting, the forecast for time t is the data value at time t-1. You can calculate naive forecasts with moving average by setting the moving average length to 1, or with single exponential smoothing by setting the weight to 1. You can use naive forecasting to establish a benchmark for your time series model. Compare the accuracy measures of the naive model and a model using a different method. If the naive model is a better fit, you shouldn't use the other model since the naive model is a better fit and is more simple.

The fitted value at time t is the uncentered moving average at time t -1. The forecasts are the fitted values at the forecast origin. If you forecast 10 time units ahead, the forecasted value for each time will be the fitted value at the origin. Data up to the origin are used for calculating the moving averages.

You can use the linear moving averages method by calculating consecutive moving averages. The linear moving averages method is often used when there is a trend in the data. First, calculate and store the moving average of the original series. Then, calculate and store the moving average of the previously stored column to obtain a second moving average.

In naive forecasting, the forecast for time t is the data value at time t -1. Using moving average procedure with a moving average of length one gives naive forecasting.

The fitted value at time t is the smoothed value at time t-1. The forecasts are the fitted value at the forecast origin. If you forecast 10 time units ahead, the forecasted value for each time will be the fitted value at the origin. Data up to the origin are used for the smoothing.

In naive forecasting, the forecast for time t is the data value at time t-1. Perform single exponential smoothing with a weight of one to do naive forecasting.

Double exponential smoothing uses the level and trend components to generate forecasts. The forecast for m periods ahead from a point at time t is

L_t + mT_t, where L_t is the level and T_t is the trend at time t.

Data up to the forecast origin time will be used for the smoothing.

Winters' method uses the level, trend, and seasonal components to generate forecasts. The forecast for m periods ahead from a point at time t is:

L_t + mT_t

where L_t is the level and T_t is the trend at time t, multiplied by (or added to for an additive model) the seasonal component for the same period from the previous year.

Winters' Method uses data up to the forecast origin time to generate the forecasts.