Endpoints Issue in Time Series Adjusting
Olga Vasyechko, Michel Grun-Réhomme · DOAJ (DOAJ: Directory of Open Access Journals) · 2015
Time series analysis aims to reduce the effects of random variations in order to extract meaningful statistics from the data. There are many methods for time series decomposition, to be chosen by a statistician according to his/her experience . To estimate a seasonally-adjusted time series, the most common tool is moving averages The paper contributes to the issue of a choice by examining the properties of different moving average methods This paper analyzes endpoints’ smoothing of the time series following the Henderson technique and proposes a new technique to treat the endpoints based on Epanechnikov kernel . The kernel method is generally used to estimate the density of a probability distribution of a sample, taking into account the local character of this density. The main advantage of this kernel approach is that the current value has a larger weight, while the weights of past and future values decrease, when moving away from the present value . Such a property remains also valid for asymmetric moving averages . The greatest weight at the current date allows showing the most recent variations For the kernel approaches, two elements remain constant: 1. In the method which keeps the parabolas, a shift takes place between asymmetric moving averages of order 9-3 and those of order 10-2, when we move from a concave curve to a convex curve . A concave curve attributes a dominant weight coefficient to the current value that seems to be reasonable A convex curve attributes the largest weight to the last observed value, which is less reasonable 2 . With the kernel method which keeps only constants, the largest weight is always the weight of the current value and the weights decrease as we move away from the current value This suggests that for the last values, it may be better to take moving averages which keep only constants (even the straight lines); otherwise the last observed values are over-weighted and strongly influence the trend This is in contrast to the definition of a trend, which describes the long-term evolution of the series and must be relatively robust