Category: Time Series Models

Exponential smoothing algorithms are a class of widely used forecasting methods that were born on the basis of heuristic insight. Originally, they lacked a proper statistical background, unlike the more sophisticated time series models that we outline in Section 11.6. More recently, attempts to justify exponential smoothing have been put forward, but the bottom line is that…

In choosing the time window k, we have to consider a tradeoff between If k is large, the method has a lot of inertia and is not significantly influenced by occasional variability; however, it will be slow to adapt to systematic changes. On the contrary, if k is low, the algorithm will be very prompt, but also very nervous and…

Moving average is a very simple algorithm, which serves well to illustrate some tradeoffs that we will face later. As a forecasting tool, it can be used when we assume that the underlying data generating process is simply This is the model we obtain from (11.13) if we do not consider trend and seasonality.8 In plain words,…

The general idea behind time series models is that the data-generating process consists of two components: Some smoothing mechanism should be designed in order to filter errors and expose the underlying pattern. The simplest decomposition scheme we may adopt is where  is a random variable with expected value 0. Additional assumptions, for the sake of statistical…

As will be clear from the following, when we want to apply certain forecasting algorithms, we might need to fit one or more parameters used to calculate a forecast. This is typically done by a proper initialization. When the algorithm depends on estimates of parameters, if we start from scratch, initial performance will be poor…

cBefore we delve into forecasting algorithms, it is fundamental to understand how we may evaluate their performance. This issue is sometimes overlooked in practice: Once a forecast is calculated and used to make a decision, it is often thrown away for good. This is a mistake, as the performance of the forecasting process should be…

When learning about forecasting algorithms, it is easy to get lost in technicalities and forget a few preliminary points. Forecasting is not about a single number. We are already familiar with inferential statistics and confidence intervals. Hence, we should keep in mind that a single number, i.e., a point forecast, may be of quite little…

Forecasting is a common task in business management. Simple linear regression models, we have met a kind of statistical model that can be used as a forecasting tool, provided that Even though, strictly speaking, linear regression captures association and not causation, the idea behind such a model is that knowledge about explanatory variables is useful…