Autoregressive Models The autoregressive model is one of a group of linear prediction formulas that attempt to predict an output y[n] of a system based on the previous outputs ( y[n-1]‚y[n-2]...) and inputs ( x[n]‚ x[n-1]‚ x[n-2]...). Deriving the linear prediction model involves determining the coeffiecients a1‚a2‚.. and b0‚b1‚b2‚... in the equation: ye[n] (estimated) = a1*y[n-1] + a2*y[n-2]... + b0*x[n] + b1*x[n-1] + ... Note the REMARKABLE similarity between the prediction formula and the
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Chapter Chapter 12 Autoregressive Conditional Heteroscedasticity (ARCH) and Generalized ARCH (GARCH) Models Section Section 12.1 Introduction ARCH and GARCH Models • ARCH and GARCH models are designed to model heteroscedasticity (unequal variance) of the error term with the use of timeseries data • Objective is to model and forecast volatility Example: Understand the risk of holding an asset; useful in financial situations • ARCH -- Autoregressive Conditional Heteroscedasticity
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An actuary uses a time series to estimate the average claim severity next year as $10‚000. We use this forecast to set rates for auto insurance policies. The procedure used to estimate the future average claim severity may be unbiased‚ bu the actual claim severity next year will not be exactly $10‚000. If the actuary’s estimate is a normal distribution with a mean of $10‚000 and a standard deviation of $500‚ we are 95% confident that the true average claim severity will lie between $9‚000 and $11
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Time series models Time series is an ordered sequence of values of a variable at equally spaced time intervals. Time series occur frequently when looking at industrial data. The essential difference between modeling data via time series methods and the other methods is that Time series analysis accounts for the fact that data points taken over time may have an internal structure such as autocorrelation‚ trend or seasonal variation that should be accounted for. A Time-series model explains a variable
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Department of Water and Health‚ JSS University‚ Mysore‚ Karnataka ARTICLE INFO Article History: Received 20 November‚ 2012 Received in revised form 14th December‚ 2012 Accepted 21th January‚ 2013 Published online 14th February‚ 2013 th ABSTRACT Stochastic Models have been used to analyze the inflow rate of wastewater to the sewage treatment plant (STP) of Southern Mysore. Based on the daily inflow data of 217 days (November 2011 to June 2012)‚ many possible combinations of the orders ‘p’ and ‘q’ were made
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Abstract This paper is to employ a vector autoregressive model to investigate the impact of stock market and saving rate on GDP growth. The result indicates that the lagged values of both stock index and saving rate don’t have influence on the current value of GDP. However‚ we find that the lagged value of stock index does have impact on saving rate. We conclude that one of the most important reason lead to this result should due to small sample size and data of saving rate still remains non-stationary
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analysis appropriate ARMA model was determined using correlogram and information criteria as well‚ and applied to the consumption data only. These models (ARMA and ARIMA models) are built up from the white noise process. We use the estimated autocorrelation and partial autocorrelation functions of the series to help us select the particular model that we will estimate to help us forecast the series. Second step of data analysis was comprised of co-integration and Error Correction model. It was found that
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Visiting Professor at Northeastern Illinois University‚ Chicago Financial Mathematics Mathematics Department at Northeastern Illinois University‚ Chicago Wednesday‚ October 3rd‚ 2012 1 Agenda • Approaches to Modeling Volatilities • Volatility Models in Capital Allocation - VaR • Application of GARCH to Modeling Volatility • Volatility Impacts Option Value • Portfolio Hedging Against Volatility Change 2 Standard Approach to Estimating Volatility • Define sn as the volatility per day
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Box-Jenkins Modeling and Forecasting of Monthly Electric Consumption of PANELCO III Customers ______________________________ A Special Problem Presented To The Panel of Evaluators Mathematics Department Pangasinan State University Urdaneta City _______________________________ In Partial Fulfillment of The Requirement for the Degree of Bachelor of Science in Mathematics Major in Statistics ______________________________ By: Jake Anthony E. CantubaMarch 2014 APPROVAL SHEET In partial
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SERIES ANALYSIS Chapter Three Univariate Time Series Models Chapter Three Univariate time series models c WISE 1 3.1 Preliminaries We denote the univariate time series of interest as yt. • yt is observed for t = 1‚ 2‚ . . . ‚ T ; • y0‚ y−1‚ . . . ‚ y1−p are available; • Ωt−1 the history or information set at time t − 1. Call such a sequence of random variables a time series. Chapter Three Univariate time series models c WISE 2 Martingales Let {yt} denote a sequence
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