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    Econometrics II CH 2

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    nigusu degu
    This document is the contents page and introduction for Chapter 2 of an econometrics textbook. It outlines the key topics that will be covered in the chapter, including data generating processes in time series, stationarity and nonstationarity, spurious regression, cointegration, vector autoregressive models, and applications in STATA. The introduction defines time series data and notes that when collecting such data, we only observe a single realization of the stochastic process due to the inability to rerun history. It also discusses how time series samples and populations relate to cross-sectional concepts.

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    Econometrics II CH 2

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    nigusu degu
    552 views18 pages
    This document is the contents page and introduction for Chapter 2 of an econometrics textbook. It outlines the key topics that will be covered in the chapter, including data generating processes in time series, stationarity and nonstationarity, spurious regression, cointegration, vector autoregressive models, and applications in STATA. The introduction defines time series data and notes that when collecting such data, we only observe a single realization of the stochastic process due to the inability to rerun history. It also discusses how time series samples and populations relate to cross-sectional concepts.

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    Econometrics II Ch 2 ppt

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    This document is the contents page and introduction for Chapter 2 of an econometrics textbook. It outlines the key topics that will be covered in the chapter, including data generating processes in time series, stationarity and nonstationarity, spurious regression, cointegration, vector autoregressive models, and applications in STATA. The introduction defines time series data and notes that when collecting such data, we only observe a single realization of the stochastic process due to the inability to rerun history. It also discusses how time series samples and populations relate to cross-sectional concepts.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    552 views18 pages

    Econometrics II CH 2

    Uploaded by

    nigusu degu
    This document is the contents page and introduction for Chapter 2 of an econometrics textbook. It outlines the key topics that will be covered in the chapter, including data generating processes in time series, stationarity and nonstationarity, spurious regression, cointegration, vector autoregressive models, and applications in STATA. The introduction defines time series data and notes that when collecting such data, we only observe a single realization of the stochastic process due to the inability to rerun history. It also discusses how time series samples and populations relate to cross-sectional concepts.

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    © All Rights Reserved
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    You are on page 1of 18

    Econometrics II

    Chapter two

    Abebe Mucheye Kassie ( M.Sc.)


    Department of Economics
    Debre Markose University

    1
    Contents of the Chapter

     Data generating process in time series


     Stationarity and nonstationarity of time series
     Spurious regression
     Cointegration and error correction mechanism: the E-G
    approach
     Introduction to vector autoregressive (VAR)
     Cointegration and error correction mechanism: the
    Johansen approach
     Applications using STATA

    2
    Introduction
     Time series: Observations on income, consumption, interest rates,
    etc over a number of time periods (years, quarters, months, …)
     A set of random variables indexed by time (such as Yt) called a
    stochastic process or random process or time series process.
     When we collect time series data, we obtain only one possible
    outcome of the stochastic process (called realization).
     We can only see a single realization b/c we cannot go back in time &
    start the process over again.
     This is analogous to collecting one random sample in cross sectional
    analysis.
     Realization in time series = sample in cross section
     . The set of all possible realizations in time series is akin to
    population in cross section.
     Sample size in time series is the number of time periods over which
    we observe the variables of interest (or see their realizations). 3
    Cont..
     If we let Y denote a random variable, and if it is
    continuous, we denote it as Y(t), but if it is discrete, we
    denoted it as Yt.
     An example of the former is an electrocardiogram, and an
    example of the latter is GDP, PDI, etc.
     Since most economic data are collected at discrete points
    in time, for our purpose we will use the notation Yt rather
    than Y(t).
     If we let Y represent GDP, for our data we have Y1, Y2, Y3,
    ... , Y86, Y87, Y88 , where the subscript 1 denotes the first
    observation (i.e., GDP for the first quarter of 1970) and the
    subscript 88 denotes the last observation (i.e., GDP for the
    fourth quarter of 1991).
    4
    Data generating process in time series
     The main objective of time series modeling is to forecast,
    interpret & test hypotheses concerning economic data.
    In forecasting, we decompose a time series into four
    components:
     Trend component - it is non-stochastic;
     Seasonal component - it is non-stochastic;
     Cyclical component - it is non-stochastic;
     Irregular component - it is stochastic.
     Since the irregular component is stochastic, the goal of the
    econometrician is to model this component.

    5
    Data generating process in time series
     Let Yt denotes data series at time t .
    Suppose the difference equations used to construct
    components of the Yt series are:
    Trend: Tt = 1 + 0.1t
    Seasonal: St = 1.6 Si n(tπ/8)
    Irregular: It = 0.7It
    where ut is white noise.
     The generated series for t = 100 are presented as follows.

    6
    Data generating process in time series

    7
    Data generating process in time series

    8
    Data generating process in time series
    White noise & Random walk processes

    9
    White noise & Random walk processes

    10
    Stationarity and nonstationarity of time series

    11
    12
    13
    Stationarity and nonstationarity of time series

    14
    Cont.…

    15
    Integrated time series

    16
    Integrated time series Theorem

    17
    Testing stationarity: Unit root tests

    18

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