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Sekar, P.
- Diagnostic Checking of Time Series Models
Abstract Views :362 |
PDF Views:106
Authors
P. Sekar
1
Affiliations
1 Department of Mathematics, Pachaiyappa’s College for Men, Kancheepuram–631 501, TN, IN
1 Department of Mathematics, Pachaiyappa’s College for Men, Kancheepuram–631 501, TN, IN
Source
Indian Journal of Science and Technology, Vol 3, No 9 (2010), Pagination: 1026-1031Abstract
Diagnostic checks have become a standard tool for identification of models before forecasting the data. The overall test for lack of fit for autoregressive moving average models proposed by Box and Pierce (1970) and a measure of lack of fit in time series models proposed by Ljung and Box (1978) are considered. In this paper, a modification is made and it is shown that a substantially improved approximation results from a simple improvement of this test. Cumulative periodogram check is also given.Keywords
Time Series, ARMA, ARIMA, ForecastingReferences
- Abraham B and Vijayan K (1988) A statistic to check model adequacy in time series. Comm. Statist. Theory Methods. 17(12), 4271-4278.
- Anders Milhqj (1981) A test of fit in time series models. Biometrika, 68, 1, 177-87.
- Anderson RL (1941) Distribution of the time serial correlation coefficients. Ann. Math. Stat. 8(1), 1-13.
- Bartlett MS (1946) On the theoretical specification of sampling properties of autocorrelated time series. J. Royal Stat. Soc. Ser B. 8, 27-41.
- Box GEP and Jenkins GM (1976) Time series analysis: forecasting and control. Revised edition, San Francisco: Holden-day.
- Box GEP and Pierce DA (1970) Distribution of residual autocorrelation in autoregressive integrated moving average models. J. Amer. Stat. Assoc. 64, 1509-1526.
- Box GEP, Jenkins GM and Reinsel GC (1994) Time series analysis: forecasting and control, 3rd edition, Prentice Hall, New Jersey.
- Brockwell BJ and Davis RA (1991) Time series: theory and methods, 2nd edition, Springer-Verlag, New York.
- Davies N, Triggs CM and Newbold P (1977) Significance levels of the Box-Pierce Portmanteau statistic in finite samples. Biometrika. 64(3), 517-522.
- Godfrey LG (1979) Testing the adequacy of a time series model. Biometrika. 66, 67-72.
- Hokstad P (1983) A method for diagnostic checking of time series models. J. Time Ser. Anal. 4(3), 177-183.
- Jenkins GM and Watts DG (1968) On the theoretical specification of sampling properties of autocorrelated time series. J. Royal Stat. Soc. B8, 27.
- Jenkins GM and Watts DG (1969) Spectral analysis and its applications, Holden-day series in time series analysis, San Francisco, California.
- Ljung GM (1986) Diagnostic testing of univariate time series models. Biometrika. 73(3), 725-730.
- Ljung GM and Box GEP (1978) On a measure of lack of fit in time series models. Biometrika. 65, 297-303.
- McLeod AI (1994) Diagnostic checking of periodic auto regression models with application. J. Time Ser. Anal. 15(2), 221-233.
- McLeod AI and Li WK (1983) Diagnostic checking ARMA time series models using squared-residual autocorrelation. J. Time Ser. Anal. 4(4), 269-273.
- Smith JQ (1985) Diagnostic checks of non-standard time series models. J. Forecasting. 4, 283-291.
- Application of Time Series Models
Abstract Views :360 |
PDF Views:95
Authors
P. Sekar
1
Affiliations
1 Department of Mathematics, Pachaiyappa’s College for Men, Kancheepuram–631 501, TN, IN
1 Department of Mathematics, Pachaiyappa’s College for Men, Kancheepuram–631 501, TN, IN
Source
Indian Journal of Science and Technology, Vol 3, No 9 (2010), Pagination: 1032-1037Abstract
Forecasting is an ultimate aim in the study of time series analysis. Anyone who is engaged in planning, controlling and managing projects, personnel, finance and operations will be interested in knowing what will happen in future with the analysis of the available dataKeywords
Time Series, ARMA, ARIMA, ARARMA, Fractional DifferencingReferences
- Box GEP and Jenkins GM (1976) Time series analysis: forecasting and control, revised edn, San Francisco: Holden-day.
- Hosking JRM (1981) Fractional differencing. Biometrika, 68(1), 165-176.
- Montgomary DC and Johnson LA (1976) Forecasting and time series analysis. McGraw Hill Inc., San Francisco. pp: 231-232.
- Parzen E (1982) ARARMA models for time series analysis and forecasting. J. Forecasting. 1, 67-82.
- Sekar P and Sreenivasan M (1996) Simulation and modeling of time series using fractional differencing. Proc. of Int. Conf. on Stochastic Process. Dec. 26-29, Cochin, India, pp:225-233.
- Assessment of Optimal Combination of Operating Parameters using Graph Theory Matrix Approach
Abstract Views :189 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics, Saveetha School of Engineering, Saveetha University, Chennai - 602105, Tamil Nadu, IN
2 Department of Physics, Saveetha School of Engineering, Saveetha University, Chennai - 602105, Tamil Nadu, IN
3 Department of Mathematics, C. Kandaswami Naidu College for Men, Anna Nagar, Chennai – 600102, Tamil Nadu, IN
1 Department of Mathematics, Saveetha School of Engineering, Saveetha University, Chennai - 602105, Tamil Nadu, IN
2 Department of Physics, Saveetha School of Engineering, Saveetha University, Chennai - 602105, Tamil Nadu, IN
3 Department of Mathematics, C. Kandaswami Naidu College for Men, Anna Nagar, Chennai – 600102, Tamil Nadu, IN
Source
Indian Journal of Science and Technology, Vol 9, No 36 (2016), Pagination:Abstract
Background/Objectives: Graph theory matrix approach is a logical and systematical approach originated from combinatorial mathematics. Graph theory matrix approach is adopted to find the optimal combination of operating parameters. Methods/Statistical Analysis: Graph theory matrix approach helps to analyze and understand the system as a whole by identifying system and sub-system up to the component level. Attributes digraph is developed to represent the inheritance and the interdependencies of the subsystems. Matrix method is adopted to convert the digraph into mathematical form. Permanent function is deduced to determine the parameter index to find the optimal combination of operating parameters on a diesel engine. Findings: The combination of 18 Ampere load, 270 BTDC Injection timing and 200 bar Injection pressure forms the optimal combination of operating parameters having the highest value of Permanent index. Applications/Improvements: Graph theory matrix approach offers simple, generic, easy and convenient computation. It finds applications in the fields of education, neural networks, automotive industry, manufacturing, electronic devices, total quality management, location of plants, supply chain management, information technology, human resource selection etc.Keywords
Engine, Graph Theory, Matrix Approach, Operating Parameter, Permanent Index.- Graph Theory Matrix Approach – A Review
Abstract Views :173 |
PDF Views:0
Authors
N. K. Geetha
1,
P. Sekar
1
Affiliations
1 Department of Mathematics, C. Kandaswami Naidu College for Men, Anna Nagar, Chennai - 600102, IN
1 Department of Mathematics, C. Kandaswami Naidu College for Men, Anna Nagar, Chennai - 600102, IN