A non‐linear dynamic model for multiplicative seasonal‐trend decomposition

Ozaki, Tohru; Thomson, Peter

doi:10.1002/for.816

“…Finally, the methodology of Ozaki and Thomson (1994) is close to our non‐linear UC model of below although the specifics and motivations of the models are different. Ozaki and Thomson considered a UC model in levels, given by where M t is a linear Gaussian stochastic process for the trend whereas G t is a stochastic seasonal component.…”

Section: Seasonal Interacting Componentsmentioning

confidence: 97%

Seasonality with Trend and Cycle Interactions in Unobserved Components Models

Koopman¹,

Lee²

2009

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary. Unobserved components time series models decompose a time series into a trend, a season, a cycle, an irregular disturbance, and possibly other components. These models have been successfully applied to many economic time series. The standard assumption of a linear model, often appropriate after a logarithmic transformation of the data, facilitates estimation, testing, forecasting and interpretation. However, in some settings the linear-additive framework may be too restrictive. In this paper, we formulate a non-linear unobserved components time series model which allows interactions between the trend-cycle component and the seasonal component. The resulting model is cast into a non-linear state space form and estimated by the extended Kalman filter, adapted for models with diffuse initial conditions. We apply our model to UK travel data and US unemployment and production series, and show that it can capture increasing seasonal variation and cycle dependent seasonal fluctuations.

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“…Edmundson (1990), Choi and Wohar (1995), Ozarki and Thompson (2002), and Webby, O'Connor, and Edmundson (2005) found that time‐series forecasts can be significantly improved by decomposing the series into its simplest components: trend, cycle, and noise. Decomposition of a forecasting problem has also been implemented by breaking the problem down into independent components that can be additively recombined.…”

Section: The Practice Of Business Forecastingmentioning

confidence: 99%

Decomposition as a Complex‐Skill Acquisition Strategy in Management Education: A Case Study in Business Forecasting

Adya

¹

,

Lusk

²

,

Balhadjali

³

2009

Decision Sci J Innov Edu

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Graduate business education has been criticized for utilizing simplistic teaching strategies that compromise the presentation of real-world complex skills in the classroom. In this article, we propose that complex management functions can be effectively taught using decomposition strategies. We demonstrate the usefulness of this strategy in the domain of business forecasting by comparing the forecast accuracy of students instructed in decomposition (RBF-Instructed) with that of students not exposed to such instruction (Uninstructed), as well as with an expert system called Rule-Based Forecasting (RBF). RBF-Instructed students demonstrated significant improvements over Uninstructed students and were at least as accurate as the RBF system. Our findings suggest that academics engaged in teaching complex domains can benefit from building their teaching environment on a decomposition framework. We further suggest strategies for measuring the effectiveness and endurance of classroom knowledge thus imparted. Implications for academia and practice are discussed and a research framework is proposed.

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“…Finally, the methodology of Ozaki and Thomson (1994) is close to our non-linear UC model of Section 3.2 below although the specifics and motivations of the models are different. Ozaki and Thomson considered a UC model in levels, given by…”

Section: A Review Of Non-linear Trend-seasonal Modelsmentioning

confidence: 99%

Seasonality with Trend and Cycle Interactions in Unobserved Components Models

Koopman

¹

,

Lee²

2008

View full text Add to dashboard Cite

Summary. Unobserved components time series models decompose a time series into a trend, a season, a cycle, an irregular disturbance, and possibly other components. These models have been successfully applied to many economic time series. The standard assumption of a linear model, often appropriate after a logarithmic transformation of the data, facilitates estimation, testing, forecasting and interpretation. However, in some settings the linear-additive framework may be too restrictive. In this paper, we formulate a non-linear unobserved components time series model which allows interactions between the trend-cycle component and the seasonal component. The resulting model is cast into a non-linear state space form and estimated by the extended Kalman filter, adapted for models with diffuse initial conditions. We apply our model to UK travel data and US unemployment and production series, and show that it can capture increasing seasonal variation and cycle dependent seasonal fluctuations.

show abstract

A non‐linear dynamic model for multiplicative seasonal‐trend decomposition

Cited by 6 publications

References 25 publications

Seasonality with Trend and Cycle Interactions in Unobserved Components Models

Seasonality with Trend and Cycle Interactions in Unobserved Components Models

Decomposition as a Complex‐Skill Acquisition Strategy in Management Education: A Case Study in Business Forecasting

Seasonality with Trend and Cycle Interactions in Unobserved Components Models

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