Game Of Shadows: Statistical Inferences of Projections and an Application on Macroeconomic Indicators Affecting Exchange Rates in Turkey

Abstract

The mathematical backgrounds of statistical methods used in practice can often be seen as insignificant details for those who apply them. However, they are very important techniques for different details of scientific research. For example, the least-squares method can be elaborated in three different ways. While a practitioner sees the method as the analysis button of the package program, a theorist sees the EKK method as a solution technique for a system of equations with a variable number less than the number of observations. This is also the technique of obtaining an inverted image of an element taken from the image space in a case where the image space is larger than the domain. In this respect, this study aims to give the theoretical background of techniques such as principal component analysis, Karhunen-Loeve transform, partial least squares regression, and Nipals algorithm used in research. In order to make methods understandable, the application in which USD and Euro rates are chosen as the answer variable is included in the study. Explanatory variables, on the other hand, are export, import, stock market index, unemployment rate, inflation, current account deficit, and foreign Exchange reserve variables, which are thought to be interrelated. The NIPALS algorithm was applied after multiple linear regression, NIPALS algorithm and Karhunen-Loeve transform were applied to the model, which was created by taking monthly data in the period of 2014:01/ 2021:06.