William R. Nugent
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780195369625
- eISBN:
- 9780199865208
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195369625.003.0002
- Subject:
- Social Work, Research and Evaluation
This chapter covers regression-discontinuity models for analyzing the data from single case designs. Auto-regressive-integrated-moving-average models are also described and illustrated. These ...
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This chapter covers regression-discontinuity models for analyzing the data from single case designs. Auto-regressive-integrated-moving-average models are also described and illustrated. These statistical methods are useful when there are a large number of observations in the phases of a single case design. These methods are described in detail and illustrated using data from a study of the implementation of an Aggression Replacement Training program implemented in a runaway shelter.Less
This chapter covers regression-discontinuity models for analyzing the data from single case designs. Auto-regressive-integrated-moving-average models are also described and illustrated. These statistical methods are useful when there are a large number of observations in the phases of a single case design. These methods are described in detail and illustrated using data from a study of the implementation of an Aggression Replacement Training program implemented in a runaway shelter.
Harold D. Clarke, Helmut Norpoth, and Paul Whiteley
- Published in print:
- 1998
- Published Online:
- November 2003
- ISBN:
- 9780198292371
- eISBN:
- 9780191600159
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198292376.003.0007
- Subject:
- Political Science, Reference
Extending the basic regression model to the analysis of processes, which entail modelling time. The example demonstrates using Box‐Jenkins ARIMA intervention and transfer function models, and error ...
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Extending the basic regression model to the analysis of processes, which entail modelling time. The example demonstrates using Box‐Jenkins ARIMA intervention and transfer function models, and error correction models, and introduces and interprets statistical tests such as the Q‐test and the Dickey‐Fuller t‐ratio.Less
Extending the basic regression model to the analysis of processes, which entail modelling time. The example demonstrates using Box‐Jenkins ARIMA intervention and transfer function models, and error correction models, and introduces and interprets statistical tests such as the Q‐test and the Dickey‐Fuller t‐ratio.
Ronald K. Pearson
- Published in print:
- 1999
- Published Online:
- November 2020
- ISBN:
- 9780195121988
- eISBN:
- 9780197561294
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195121988.003.0004
- Subject:
- Computer Science, Mathematical Theory of Computation
It was emphasized in Chapter 1 that low-order, linear time-invariant models provide the foundation for much intuition about dynamic phenomena in the real world. This chapter provides a brief review ...
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It was emphasized in Chapter 1 that low-order, linear time-invariant models provide the foundation for much intuition about dynamic phenomena in the real world. This chapter provides a brief review of the characteristics and behavior of linear models, beginning with these simple cases and then progressing to more complex examples where this intuition no longer holds: infinite-dimensional and time-varying linear models. In continuous time, infinite-dimensional linear models arise naturally from linear partial differential equations whereas in discrete time, infinite-dimensional linear models may be used to represent a variety of “slow decay” effects. Time-varying linear models are also extremely flexible: In the continuous-time case, many of the ordinary differential equations defining special functions (e.g., the equations defining Bessel functions) may be viewed as time-varying linear models; in the discrete case, the gamma function arises naturally as the solution of a time-varying difference equation. Sec. 2.1 gives a brief discussion of low-order, time-invariant linear dynamic models, using second-order examples to illustrate both the “typical” and “less typical” behavior that is possible for these models. One of the most powerful results of linear system theory is that any time-invariant linear dynamic system may be represented as either a moving average (i.e., convolution-type) model or an autoregressive one. Sec. 2.2 presents a short review of these ideas, which will serve to establish both notation and a certain amount of useful intuition for the discussion of NARMAX models presented in Chapter 4. Sec. 2.3 then briefly considers the problem of characterizing linear models, introducing four standard input sequences that are typical of those used in linear model characterization. These standard sequences are then used in subsequent chapters to illustrate differences between nonlinear model behavior and linear model behavior. Sec. 2.4 provides a brief introduction to infinite-dimensional linear systems, including both continuous-time and discrete-time examples. Sec. 2.5 provides a similar introduction to the subject of time-varying linear systems, emphasizing the flexibility of this class. Finally, Sec. 2.6 briefly considers the nature of linearity, presenting some results that may be used to define useful classes of nonlinear models.
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It was emphasized in Chapter 1 that low-order, linear time-invariant models provide the foundation for much intuition about dynamic phenomena in the real world. This chapter provides a brief review of the characteristics and behavior of linear models, beginning with these simple cases and then progressing to more complex examples where this intuition no longer holds: infinite-dimensional and time-varying linear models. In continuous time, infinite-dimensional linear models arise naturally from linear partial differential equations whereas in discrete time, infinite-dimensional linear models may be used to represent a variety of “slow decay” effects. Time-varying linear models are also extremely flexible: In the continuous-time case, many of the ordinary differential equations defining special functions (e.g., the equations defining Bessel functions) may be viewed as time-varying linear models; in the discrete case, the gamma function arises naturally as the solution of a time-varying difference equation. Sec. 2.1 gives a brief discussion of low-order, time-invariant linear dynamic models, using second-order examples to illustrate both the “typical” and “less typical” behavior that is possible for these models. One of the most powerful results of linear system theory is that any time-invariant linear dynamic system may be represented as either a moving average (i.e., convolution-type) model or an autoregressive one. Sec. 2.2 presents a short review of these ideas, which will serve to establish both notation and a certain amount of useful intuition for the discussion of NARMAX models presented in Chapter 4. Sec. 2.3 then briefly considers the problem of characterizing linear models, introducing four standard input sequences that are typical of those used in linear model characterization. These standard sequences are then used in subsequent chapters to illustrate differences between nonlinear model behavior and linear model behavior. Sec. 2.4 provides a brief introduction to infinite-dimensional linear systems, including both continuous-time and discrete-time examples. Sec. 2.5 provides a similar introduction to the subject of time-varying linear systems, emphasizing the flexibility of this class. Finally, Sec. 2.6 briefly considers the nature of linearity, presenting some results that may be used to define useful classes of nonlinear models.
David McDowall, Richard McCleary, and Bradley J. Bartos
- Published in print:
- 2019
- Published Online:
- February 2021
- ISBN:
- 9780190943943
- eISBN:
- 9780190943981
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190943943.001.0001
- Subject:
- Sociology, Social Research and Statistics
Interrupted Time Series Analysis develops a comprehensive set of models and methods for drawing causal inferences from time series. Example analyses of social, behavioural, and biomedical time series ...
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Interrupted Time Series Analysis develops a comprehensive set of models and methods for drawing causal inferences from time series. Example analyses of social, behavioural, and biomedical time series illustrate a general strategy for building AutoRegressive Integrated Moving Average (ARIMA) impact models. The classic Box-Jenkins-Tiao model-building strategy is supplemented with recent auxiliary tests for transformation, differencing and model selection. New developments, including Bayesian hypothesis testing and synthetic control group designs are described and their prospects for widespread adoption are discussed. Example analyses make optimal use of graphical illustrations. Mathematical methods used in the example analyses are explicated assuming only exposure to an introductory statistics course. Design and Analysis of Time Series Experiments (DATSE) and other appropriate authorities are cited for formal proofs. Forty completed example analyses are used to demonstrate the implications of model properties. The example analyses are suitable for use as problem sets for classrooms, workshops, and short-courses.Less
Interrupted Time Series Analysis develops a comprehensive set of models and methods for drawing causal inferences from time series. Example analyses of social, behavioural, and biomedical time series illustrate a general strategy for building AutoRegressive Integrated Moving Average (ARIMA) impact models. The classic Box-Jenkins-Tiao model-building strategy is supplemented with recent auxiliary tests for transformation, differencing and model selection. New developments, including Bayesian hypothesis testing and synthetic control group designs are described and their prospects for widespread adoption are discussed. Example analyses make optimal use of graphical illustrations. Mathematical methods used in the example analyses are explicated assuming only exposure to an introductory statistics course. Design and Analysis of Time Series Experiments (DATSE) and other appropriate authorities are cited for formal proofs. Forty completed example analyses are used to demonstrate the implications of model properties. The example analyses are suitable for use as problem sets for classrooms, workshops, and short-courses.
Arindam Bandyopadhyay
- Published in print:
- 2022
- Published Online:
- June 2022
- ISBN:
- 9780192849014
- eISBN:
- 9780191944260
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780192849014.003.0010
- Subject:
- Economics and Finance, Financial Economics
A large proportion of economic data is in the form of time series. For forecasting financial variables, risk analysts need to understand trend, cyclicality, seasonality, and randomness of the series. ...
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A large proportion of economic data is in the form of time series. For forecasting financial variables, risk analysts need to understand trend, cyclicality, seasonality, and randomness of the series. This chapter explains trend forecasting method that will be useful for forecasting forward looking quarterly or annual gross non-performing assets, probability of default, exchange rate, and other key factors. The auto-regressive and moving average techniques are explained to predict key balance sheet value of Reserve Bank of India. Unit root test and role of ARIMA model have been explained with detailed steps to build forecasting models for exchange rate series. The same technique can be applied to predict future default rates as well. Next, multivariate time-series model has been constructed to link default rates with macroeconomic factors to derive stress testing scenarios. Time-series forecasting techniques have numerous applications in deriving early warning signals, loss provisioning model, and stress testing bank capital.Less
A large proportion of economic data is in the form of time series. For forecasting financial variables, risk analysts need to understand trend, cyclicality, seasonality, and randomness of the series. This chapter explains trend forecasting method that will be useful for forecasting forward looking quarterly or annual gross non-performing assets, probability of default, exchange rate, and other key factors. The auto-regressive and moving average techniques are explained to predict key balance sheet value of Reserve Bank of India. Unit root test and role of ARIMA model have been explained with detailed steps to build forecasting models for exchange rate series. The same technique can be applied to predict future default rates as well. Next, multivariate time-series model has been constructed to link default rates with macroeconomic factors to derive stress testing scenarios. Time-series forecasting techniques have numerous applications in deriving early warning signals, loss provisioning model, and stress testing bank capital.
Richard McCleary, David McDowall, and Bradley Bartos
- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780190661557
- eISBN:
- 9780190661595
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190661557.001.0001
- Subject:
- Sociology, Methodology and Statistics
Design and Analysis of Time Series Experiments develops a comprehensive set of models and methods for drawing causal inferences from time series. Example analyses of social, behavioral, and ...
More
Design and Analysis of Time Series Experiments develops a comprehensive set of models and methods for drawing causal inferences from time series. Example analyses of social, behavioral, and biomedical time series illustrate a general strategy for building AutoRegressive Integrated Moving Average (ARIMA) impact models. The classic Box-Jenkins-Tiao model-building strategy is supplemented with recent auxiliary tests for transformation, differencing, and model selection. The validity of causal inferences is approached from two complementary directions. The four-validity system of Cook and Campbell relies on ruling out discrete threats to statistical conclusion, internal, construct, and external validity. The Rubin system causal model relies on the identification of counterfactual time series. The two approaches to causal validity are shown to be complementary and are illustrated with a construction of a synthetic control time series. Example analyses make optimal use of graphical illustrations. Mathematical methods used in the example analyses are explicated in technical appendices, including expectation algebra, sequences and series, maximum likelihood, Box-Cox transformation analyses and probability.Less
Design and Analysis of Time Series Experiments develops a comprehensive set of models and methods for drawing causal inferences from time series. Example analyses of social, behavioral, and biomedical time series illustrate a general strategy for building AutoRegressive Integrated Moving Average (ARIMA) impact models. The classic Box-Jenkins-Tiao model-building strategy is supplemented with recent auxiliary tests for transformation, differencing, and model selection. The validity of causal inferences is approached from two complementary directions. The four-validity system of Cook and Campbell relies on ruling out discrete threats to statistical conclusion, internal, construct, and external validity. The Rubin system causal model relies on the identification of counterfactual time series. The two approaches to causal validity are shown to be complementary and are illustrated with a construction of a synthetic control time series. Example analyses make optimal use of graphical illustrations. Mathematical methods used in the example analyses are explicated in technical appendices, including expectation algebra, sequences and series, maximum likelihood, Box-Cox transformation analyses and probability.
