“ Add your company slogan ” Analyzing a Time Series Anastasiya Maltseva e-47 LOGO
Definition A time series is a chronological sequence of observations on a particular variable. Usually the observations are taken at regular intervals (days, months, years), but the sampling could be irregular. Examples of time series are: • monthly sales at a selected store • a closing stock price each business day
Every time series consists of separate values (trend components) characterizing changes of measurements which is under examination during the particular period of time
Structure of time series Study of the structure of BP is based on component analysis or decomposition the Trend Component (value) X the Cyclical c Component t Time series the Irregular s Component t the Seasonal ε Component t
Models of time series Economic processes can be represented in the form of different models: 1 2 3 Autoregress ive model (AR) Movingaverage (MA) model Autoregressive –moving -average (ARMA) model
Autoregressive (AR) model § Autoregressive (AR) model is a type of random process which is often used to model and predict various types of natural phenomena. § The autoregressive model is one of a group of linear prediction formulas that attempt to predict an output of a system based on the previous outputs.
Autoregressive (AR) model The AR model is defined as: c, φ – coefficients of autoregression ε– white noise error terms Xi-1 – value of time series at previous time period Xi – value of time series at present moment
Autoregressive (AR) model Example MS Excel. Prediction of the value of the several periods ahead. The graph shows a pronounced trend.
Autoregressive (AR) model Make the forecast of these sales into the following 2 periods: 1) Find out autoregression - Copy with a shift in one cell of our time series and paste it in the column “C” Then calculate the autoregressive coefficients by means of data analysis, section "Regression".
Moving Average (MA) model Moving-average (MA) model is a common approach for modeling univariate time series models. θ 1, . . . , θq - the parameters of the model, μ is the expectation of Xt (often assumed to equal 0), the εt, εt-1 - white noise error terms
Moving Average (MA) model Autoregressive–moving-average (ARMA) models, sometimes called Box–Jenkins models, are typically applied to autocorrelated time series data. The model consists of two parts, an autoregressive (AR) part and a moving average (MA) part.
Moving Average (MA) model The autocorrelation of a random process describes the correlation between values of the process at different points in time, as a function of the two times or of the time difference.
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