Time Series - Econometrics - Lecture Notes, Study notes of Econometrics and Mathematical Economics

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Time Series One objective of analysing economic data is to predict or forecast future values of to build a more or less structural econometric economic variables. One approach to dot model describing the relationship between the variable of interest with other economic quantities, to estimate this model using a sample of data, and to use it as the basis for forecasting and inference For forecasting purposes, a simple model that describes the behaviour of a variable (or a set of variables) in terms of past values, without the benefit of a well developed theory, may In addition to producing forecas well prove quite satisfactory (univariate time-serie: models also produce the distribution of future values, conditional upon the past, time ser: and can thus be used to evaluate the likelihood of certain events. ‘ime Series Models Univariate A simple example is the autoregressive process of order one: AR(1) We = Cyimi + Ei, simple model can be # =1,... a sequence of iid (0,2) random variables. This very extended to allow y to depend on p past values, an AR(p), Ye = Ona + Going +... + Optimp + &s- An alternative univariate model is the moving average process, MA(1), Ye = Ey + Oey. Again this can be extended to the MA(q), Ya = Ent eu +--+ Oey The two models can be combined to generate the ARMA(p, g) model, Ye = Oya + Ggywnat ... + Opyirp beat Grew +... + Ageing Finally the extension to multivariate processes is straightforward, yy becomes an n vector is the easiest model and @ and @ become n x n matrices. The pure autoregressive proce: to handle statistically and is known as a vector autoregressive process or VAR It is possible to add a non zero constant term to all three models without altering their fundamental characteristics. The Lag Operator