Month: February 2023

MOVING AVERAGE

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,… Continue reading MOVING AVERAGE

TIME SERIES DECOMPOSITION

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… Continue reading TIME SERIES DECOMPOSITION

In- and out-of-sample checks

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… Continue reading In- and out-of-sample checks

MEASURING FORECAST ERRORS

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… Continue reading MEASURING FORECAST ERRORS

BEFORE WE START: FRAMING THE FORECASTING PROCESS

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… Continue reading BEFORE WE START: FRAMING THE FORECASTING PROCESS

Introduction

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… Continue reading Introduction

A GLIMPSE OF STOCHASTIC REGRESSORS AND HETEROSKEDASTIC ERRORS

In this section we outline what happens when we relax a bit our assumptions about the underlying statistical model: The first thing to note is that now the explanatory variable is random. This is certainly going to make things a tad more complicated, but we do not want to change our assumptions substantially, which is… Continue reading A GLIMPSE OF STOCHASTIC REGRESSORS AND HETEROSKEDASTIC ERRORS

USING REGRESSION MODELS

Regression models can be used in a variety of ways, but the essential possibilities are In the first case, we are actually concerned with the estimate of slope; the idea is that understanding the phenomenon can lead to knowledge and to better policies. Apparently, there is little difference from the second case since, after all,… Continue reading USING REGRESSION MODELS

Analysis of residuals

All of the theory we have built so far relies on specific assumptions about the errors , which we recall here once again for convenience: Since errors are not observable directly, we must settle for a check based on residuals. The check can exploit sound statistical procedures, which are beyond the scope for our purposes, it… Continue reading Analysis of residuals