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**Time Series Analysis and Forecasting on Climate Data in**Bangladesh: Time Domain Approach Presented By Dr. Md. Ayub AliProfessorDepartment of StatisticsUniversity of RajshahiMobile: 01556310294/01675001221Email: ayubali67@yahoo.com**Outline of the Presentation**• Some of the Impacts of Climate Change • One of the Main Reasons of Global warming • Basic Concept of Time Series Analysis, Model Building and Forecasting. • Some examples of Model Building on Climate data**Drought**Cyclone Storm surge, salinity Hazards Bangladesh faces Flood Water logging Bank Erosion Source: Internet**Drought, Floods, Cyclones likely to exacerbate in future due**to climate change- Country still reeling from devastation due to Cyclone Aila.Disaster risk reduction strategy need strengthening. Source: Internet**Impact of AILA …**Embankment breached during Aila remains unrepaired & water rushes inside the poldered areas Source: Internet**Impact of AILA**Source: Internet**People’s Response to Post-Aila Situation**People migrate from Kalabogi Village, Dacope Source: Internet**Global warming**Source: Internet**Green House gases**Source: Internet**Per capita emission**Source: Internet**Some possible sources for increase of carbon dioxide**Source: Internet**Approaches to forecasting**Self-projecting approach Cause-and-effect approach**Approaches to forecasting (cont.)**• Cause-and-effect approach • Advantages • Bring more information • More accurate medium-to long-term forecasts • Disadvantages • Forecasts of the explanatory time series are required • Self-projecting approach • Advantages • Quickly and easily applied • A minimum of data is required • Reasonably short-to medium-term forecasts • They provide a basis by which forecasts developed through other models can be measured against • Disadvantages • Not useful for forecasting into the far future • Do not take into account external factors**ARIMA models**• Autoregressive Integrated Moving-average • Can represent a wide range of time series • A “stochastic” modeling approach that can be used to calculate the probability of a future value lying between two specified limits**ARIMA models (Cont.)**• In the 1960’s Box and Jenkins recognized the importance of these models in the area of economic forecasting • “Time series analysis - forecasting and control” • George E. P. Box Gwilym M. Jenkins • 1st edition was in 1976 • Often called The Box-Jenkins approach**Transfer function modeling**• Yt = (B)Xt where (B) = 0 + 1B + 2B2 + ….. • B is the backshift operator BmXt = Xt - m**The Box-Jenkins model building process (cont.)**• Model identification • Autocorrelations • Partial-autocorrelations • Model estimation • The objective is to minimize the sum of squares of errors • Model validation • Certain diagnostics are used to check the validity of the model • Model forecasting • The estimated model is used to generate forecasts and confidence limits of the forecasts**Important Fundamentals**• A Normal process • Stationarity • Regular differencing • Autocorrelations (ACs) • The white noise process • The linear filter model • Invertibility**Autoregressive (AR) models**• An autoregressive model of order “p” • The autoregressive process can be thought of as the output from a linear filter with a transfer function -1(B), when the input is white noise et • The equation (B) = 0 is called the “characteristic equation”**Moving-average (MA) models**• A moving-average model of order “q” • The moving-average process can be thought of as the output from a linear filter with a transfer function (B), when the input is white noise et • The equation (B) = 0 is called the “characteristic equation”**Mixed AR and MA (ARMA) models**• A moving-average process of 1st order can be written as • Hence, if the process were really MA(1), we would obtain a non parsimonious representation in terms of an autoregressive model**Mixed AR and MA (ARMA) models (cont.)**• In order to obtain a parsimonious model, sometimes it will be necessary to include both AR and MA terms in the model • An ARMA(p, q) model • The ARMA process can be thought of as the output from a linear filter with a transfer function (B)/(B), when the input is white noise et**Identification**• Also, note that since the number of parameters (to be estimated) of each kind is almost never greater than 2, it is often practical to try alternative models on the same data. • One autoregressive (p) parameter: ACF - exponential decay; PACF - spike at lag 1, no correlation for other lags. • Two autoregressive (p) parameters: ACF - a sine-wave shape pattern or a set of exponential decays; PACF - spikes at lags 1 and 2, no correlation for other lags. • One moving average (q) parameter: ACF - spike at lag 1, no correlation for other lags; PACF - damps out exponentially. • Two moving average (q) parameters: ACF - spikes at lags 1 and 2, no correlation for other lags; PACF - a sine-wave shape pattern or a set of exponential decays. • One autoregressive (p) and one moving average (q) parameter: ACF - exponential decay starting at lag 1; PACF - exponential decay starting at lag 1.**Autoregressive conditional heteroscedastic (ARCH) model of**Engle (1982), • 2. Generalized ARCH (GARCH) model of Bollerslev (1986), • 3. GARCH-M models • 4. IGARCH models • 5. Exponential GARCH (EGARCH) model of Nelson (1991), • 6. Threshold GARCH model of Zakoian (1994) or GJR model of Glosten, Jagannathan, and Runkle (1993). • 7. Conditional heteroscedastic ARMA (CHARMA) model of Tsay (1987), • 8. Random coefficient autoregressive (RCA) model of Nicholls and Quinn (1982) • 9. Stochastic volatility (SV) models of Melino and Turnbull (1990), Harvey, Ruiz and Shephard (1994), and Jacquier, Polson and Rossi (1994).**GARCH (generalized autoregressive conditional**heteroskedasticity) • GARCH (Bollerslev, 1986) generalizes the ARCH model. Today's conditional variance is a function of past squared unexpected returns and its own past values. The model is an infinite weighted average of all past squared forecast errors, with weights that are constrained to be geometrically declining. GARCH is an ARMA(p,q) process in the variance.