New Estimation Rules for Unknown Parameters on Holt-Winters Multiplicative Method

Seng Hansun

Abstract


The Holt-Winters method is a well-known forecasting method used in time-series analysis to forecast future data when a trend and seasonal pattern is detected. There are two variations, i.e. the additive and the multiplicative method. Prior study by Vercher, et al. in [1] has shown that choosing the initial conditions is very important in exponential smoothing models, including the Holt-Winters method. Accurate estimates of initial conditions can result in better forecasting results. In this research, we propose new estimation rules for initial conditions for the Holt-Winters multiplicative method. The estimation rules were derived from the original initial conditions combined with the weighted moving average method. From the experimental results it was found that the new approach of the Holt-Winters multiplicative method can outperform the original Holt-Winters multiplicative method.

Keywords


estimation rules; Holt-Winters multiplicative method; initial conditions; time series analysis and forecasting; weighted moving average

Full Text:

PDF

References


Vercher, E., Corberan-Vallet, A., Segura, J.V. & Bermudez, J.D., Initial Conditions Estimation for Improving Forecast Accuracy in Exponential Smoothing, TOP, 20(2), pp. 517-533, 2012.

Organisation for Economic Co-operation and Development (OECD), Glossary of Statistical Terms, https://stats.oecd.org/ glossary/detail.asp? ID=2708, (10 July 2016).

Dufour, J.M., Introduction to Time Series Analysis, Research Paper, McGill University, Canada, pp. 1, 2008,

Arsham, H., Time-Critical Decision Making for Business Administration http://home.ubalt.edu/ntsbarsh/stat-data/forecast.htm, (August 20th, 2016).

Goodwin, P., The Holt-Winters Approach to Exponential Smoothing: 50 Years Old and Going Strong, FORESIGHT, pp. 30-33, 2010.

Hyndman, R.J. & Athanasopoulos, G., Forecasting: Principles and Practice, OTexts, Melbourne, Australia, 2013.

Bermudez, J.D., Segura, J.V. & Vercher, E., Holt-Winters Forecasting: An Alternative Formulation Applied to UK Air Passenger Data, Journal of Applied Statistics, 34(9), pp. 1075-1090, 2007.

Gardner, E.S., Exponential Smoothing: The State of the Art-Part II, International Journal of Forecasting, 22, pp. 637-666, 2006.

Ord, J.K., Koehler, A.B. & Snyder, R.D. Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models, Journal of the American Statistical Association, 92(440), pp. 1621-1629, 1997.

Hyndman, R.J., Koehler, A.B., Snyder, R.D. & Grose, S., A State Space Framework for Automatic Forecasting using Exponential Smoothing Methods, International Journal of Forecasting, 18, pp. 439-454, 2002.

Segura, J.V. & Vercher, E., A Spreadsheet Modeling Approach to the Holt-Winters Optimal Forecasting, European Journal of Operational Research, 131, pp. 375-388, 2001.

Bermudez, J.D., Segura, J.V. & Vercher, E., Improving Demand Forecasting Accuracy using Nonlinear Programming Software, Journal of the Operational Research Society, 57(1), pp. 94-100, 2006.

Hansun, S., A New Approach of Moving Average Method in Time Series Analysis, Proceedings of IEEE International Conference on New Media (CoNMedia), Indonesia, pp. 1-4, 2013.

Hansun, S., A New Approach of Brown’s Double Exponential Smoothing Method in Time Series Analysis, Balkan Journal of Electrical & Computer Engineering, 4(2), pp. 75-78, 2016.

Hansun, S. & Subanar, H-WEMA: A New Approach of Double Exponential Smoothing Method, TELKOMNIKA, 14(2), pp. 772-777, 2016.

NIST/SEMATECH, e-Handbook of Statistical Methods, Triple Exponential Smoothing, http://www.itl.nist.gov/div898/handbook/pmc/ section4/pmc435.htm, (15 August 2016).

Trubetskoy, G., Holt-Winters Forecasting for Dummies – Part III, http://grisha.org/blog/2016/02/17/triple-exponential-smoothing-forecasting-part-iii/, (July 30th, 2016).

Shcherbakov, M.V., Brebels, A., Shcherbakova, N.L., Tyukov, A.P., Janovsky, T.A. & Kamaev, V.A., A Survey of Forecast Error Measures, World Applied Sciences Journal, 24, pp. 171-176, 2013.

Ren, L.Y. & Ren, P., Revised Mean Absolute Percentage Errors (MAPE) on Errors from Simple Exponential Smoothing Methods for Independent Normal Time Series, Proceedings of SWDSI, Oklahoma, USA, pp. 602-611, 2009.

Lawrence, K.D., Klimberg, R.K. & Lawrence, S.M., Fundamentals of Forecasting using Excel, Industrial Press, Inc., New York, 2009.

Hyndman, R.J. & Koehler, A.B., Another Look at Measures of Forecast Accuracy, International Journal of Forecasting, 22, pp. 679-688, 2006.

Hyndman, R.J., Another Look at Forecast-Accuracy Metrics for Intermittent Demand, FORESIGHT, 4, pp. 43-46, 2006.

United States Census Bureau, Time Series Data – Monthly & Annual Retail Trade, https://www.census.gov/retail/marts/ www/timeseries.html, (22 August 2016).




DOI: http://dx.doi.org/10.5614%2Fj.math.fund.sci.2017.49.2.3

Refbacks

  • There are currently no refbacks.


View my Stats

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.