# Stationary and nonstationary time series processes

### فهرست عناوین اصلی در این پاورپوینت

● Centre for Central Banking Studies
Bank of England
● Introduction
● Structure
● Stationary and nonstationary time series processes
● Basic Stochastic Processes
● Mean, variance and autocorrelations of a weekly stationary variable
● Identifying difference stationary process: unit roots tests
● Spurious regression and cointegration
● Unrestricted VARs, near-VARs and Structural VAR (SVAR) models
● Modelling Changing Volatility
● Conditional and unconditional moments
● ARCH Processes
● Modelling ARCH processes
● GARCH Processes
● Identification and estimation of ARCH/GARCH models
● The ARCH LM-test
● GARCH Simulations
● GARCH Simulation 2
● Some GARCH Extensions
● Multivariate (MVGARCH) models
● Other MVGARCH Models
● Software and computational issues in GARCH modelling
● Summary

 نوع زبان: انگلیسی حجم: 0.28 مگا بایت نوع فایل: اسلاید پاورپوینت تعداد اسلایدها: 50 صفحه سطح مطلب: نامشخص پسوند فایل: ppt گروه موضوعی: زمان استخراج مطلب: 2019/05/17 06:22:33

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### عبارات مهم استفاده شده در این مطلب

time, model, series, stationary, variable, ., error, d, process, cointegration, correction, mean,

توجه: این مطلب در تاریخ 2019/05/17 06:22:33 به صورت خودکار از فضای وب آشکار توسط موتور جستجوی پاورپوینت جمع آوری شده است و در صورت اعلام عدم رضایت تهیه کننده ی آن، طبق قوانین سایت از روی وب گاه حذف خواهد شد. این مطلب از وب سایت زیر استخراج شده است و مسئولیت انتشار آن با منبع اصلی است.

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عبارات پرتکرار و مهم در این اسلاید عبارتند از: time, model, series, stationary, variable, ., error, d, process, cointegration, correction, mean,

### مشاهده محتوای متنیِ این اسلاید ppt

centre for central banking studies bank of england time series modelling in central banks an application of arch and garch models ibrahim stevens centre for central banking studies bank of england may ۲ ۴ introduction objective overview of time series modelling techniques modelling of volatility clustering motivation understanding the properties of macroeconomic time series used in central banks information extraction to support monetary and financial stability policy decisions option pricing extreme value theory markets asset correlations event studies risk calibration structure review of key results in econometric time series stationary and nonstationary time series processes spurious regressions and cointegration and vector autoregressions vars models of changing volatility autoregressive conditional heteroscedasticity arch generalised arch garch stationary and nonstationary time series processes economic time series data obtained from observations of an economic variable over time e.g. interest rates stock prices price indices gdp inflation….. a time series is a stochastic process a sequence of random variables rvs we use means variances and covariances to capture most of the information about the probabilistic structure of time series a time series is weakly or covariance stationary if its probability distribution does not change with time constant mean constant variance covariances stationary time series fluctuate around a constant level two types of stationary variables trend stationary differenced stationary difficult to distinguish between the two variables that needs to be ‘de trended’ or ‘differenced’ to achieve stationarity are nonstationary to de trend a series subtract if from a time trend if a time series is integrated or order d i d it has to be differenced at least d times to make it stationary integrated series are called unit root processes basic stochastic processes autoregressive ar models moving average ma models autoregressive moving average arma models white noise wn process a zero mean constant variance and no autocorrelation is said to be iid identically and independently distributed – stationary process random walks rw widely used in econometric time series in a rw the changes in the levels of the series is determined by the addition of a random error term rws may contain a drift term stochastic processes are estimated in eviews using the ar and ma functions in the equation window two important properties of rws markov property only current information is relevant in determining the conditional probability of the future value of the rv martingale the conditional expectation of the future value of a rv is the current value. however a martingale need not have a constant variance of independent errors. a rw plus a drift is therefore a martingale a positive drift term sub martingale a negative drift term is a super martingales practical applications are stock prices a rw rw and the efficient markets hypothesis rational expectations mean variance and autocorrelations of a weekly stationary variable consider a simple ar ۱ model the mean the variance the autocorrelation function acf where k is the is the number of lags and is the sample mean the acf is simple a regression of the variable on a constant and its k period lagged variables the partial autocorrelation function pacf usually calculated by fitting autoregressive models of increasing order and taking the last coefficient in each model as the sample pacf. a cut off is determined by the ljung box q test q stats is the standard test of the significance of acf with the null of zero autocorrelation available in eviews identifying difference stationary process unit roots tests recall a time series y is integrated of the order d denoted as y ~ i d if it has to be differenced d times to make it stationary δd yt a non stationary differenced time series contains at least on unit root several methods are available to test for unit roots augmented dickey fuller phillips perron kwiatkowski phillips schmidt shin kpss other issues structured breaks arch effects stock prices are integrated unit roots but stock returns are stationary spurious regression and cointegration spurious regressions regressing two non stationary variables against each other contravenes the assumptions of the classical regression model stationary variables plus zero mean and constant variance innovation term …..produces biased standard errors….. … ….and thus biased hypothesis testing likely to reject a false null hypothesis and thus accept an incorrect relationship – without any economic meaning models with high r۲ and low durbin watson statistics cointegration stationarity means that a variable is in statistical equilibrium the link between nonstationary variables and long run economic equilibrium is know as cointegration formalised in engle and granger ۱۹۸۷ two variables are said to be cointegrated of order d b denoted ci d b if they are both i d and there exist some  cointegrating parameter such that when b ۱ and d ۱ et ~۱ cointegration and error correction model cointegrated processes embody and error correction mechanism engle and granger ۱۹۸۷ suggest the following procedure stage ۱ estimate a long run cointegrating regression and test for cointegration residual based cointegration test ut ~ i use mackinnon ۱۹۹۱ critical values instead available in eviews stage ۲ if two variables are cointegrated they have a valid error correction model construct the following error correction model with ۱ and ۲ ≠ the speed of adjustment parameters the error correction is due to what is known as the granger representation theorem a cointegrated system can be represented in autoregressive moving average or error correction form but not as a var in the differenced variable due mainly to the fact that vector ma vma models are noninvertible the ma terms contain a unit root . however this is a problem rectified by the inclusion of the long run error correction term in the error correction model above. multivariate extensions johansen’s cointegrating var model the default cointegration method in eviews – johansen ۱۹۸۸ and johansen and juselius ۱۹۹ vector error correction models vecm combine short run dynamic model information with long run static model information practical issues in cointegration and ecm’s on average in each period a proportion of disequilibrium from the previous period is corrected otherwise …

### کلمات کلیدی پرکاربرد در این اسلاید پاورپوینت: time, model, series, stationary, variable, ., error, d, process, cointegration, correction, mean,

این فایل پاورپوینت شامل 50 اسلاید و به زبان انگلیسی و حجم آن 0.28 مگا بایت است. نوع قالب فایل ppt بوده که با این لینک قابل دانلود است. این مطلب برگرفته از سایت زیر است و مسئولیت انتشار آن با منبع اصلی می باشد که در تاریخ 2019/05/17 06:22:33 استخراج شده است.