Timeseriesanalysis时间序列统计方法.docVIP

CHAPTER 15 Time Series Analysis page 651 15. Introduction page 651 Chapter 15 deals with the basic components of time series, time series decomposition, and simple forecasting. At the end of this chapter, you should know the following: The four possible components of a time series. How to use smoothing techniques to remove the random variation and identify the remaining components. How to use the linear and quadratic regression models to analyze the trend. How to measure the cyclical effect using the percentage of trend method. How to measure the seasonal effect by computing the seasonal indices. How to calculate MAD and RMSE to determine which forecasting model works best. Definition A time series is a collection of data obtained by observing a response variable at periodic points in time. Definition If repeated observations on a variable produce a time series, the variable is called a time series variable. We use Yi to denote the value of the variable at time i. Four possible components: Trend ( secular trend) -- Long term pattern or direction of the time series Cycle ( cyclical effect) -- Wavelike pattern that varies about the long-term trend, appears over a number of years e.g. business cycles of economic boom when the cycle lies above the trend line and economic recession when the cycle lies below the secular trend. Seasonal variation -- Cycles that occur over short periods of time, normally 1 year e.g. monthly, weekly, daily. Random variation ( residual effect) --Random or irregular variation that a time series shows Could be additive: Yi = Ti + Ci + Si + Ii or multiplicative: Yi = Ti x Ci x Si xIi Forecasting using smoothing techniques The two commonly used smoothing techniques for removing random variation from a time series are moving averages and exponential smoothing. Moving average: ( MA) Moving averages involve averaging the time series over a specified number of periods. We usually choose odd number of periods