b denotes trend at time point t and it is sum of two

Similar documents
Chapter 15. Time Series: Descriptive Analyses, Models, and Forecasting

Types of Exponential Smoothing Methods. Simple Exponential Smoothing. Simple Exponential Smoothing

Time series Decomposition method

LINEAR TIME SERIES ANALYSIS

TIME DELAY BASEDUNKNOWN INPUT OBSERVER DESIGN FOR NETWORK CONTROL SYSTEM

Smoothing. Backward smoother: At any give T, replace the observation yt by a combination of observations at & before T

Summer Term Albert-Ludwigs-Universität Freiburg Empirische Forschung und Okonometrie. Time Series Analysis

OBJECTIVES OF TIME SERIES ANALYSIS

THE FINITE HAUSDORFF AND FRACTAL DIMENSIONS OF THE GLOBAL ATTRACTOR FOR A CLASS KIRCHHOFF-TYPE EQUATIONS

PROC NLP Approach for Optimal Exponential Smoothing Srihari Jaganathan, Cognizant Technology Solutions, Newbury Park, CA.

Lecture 3: Exponential Smoothing

Linear Combinations of Volatility Forecasts for the WIG20 and Polish Exchange Rates

Introduction to Numerical Analysis. In this lesson you will be taken through a pair of techniques that will be used to solve the equations of.

1 Widrow-Hoff Algorithm

FORECASTING THE FINANCIAL RETURNS FOR USING MULTIPLE REGRESSION BASED ON PRINCIPAL COMPONENT ANALYSIS

In this paper the innovations state space models (ETS) are used in series with:

2.1 Level, Weight, Nominator and Denominator of an Eta Product. By an eta product we understand any finite product of functions. f(z) = m.

Filtering Turbulent Signals Using Gaussian and non-gaussian Filters with Model Error

Application of Homotopy Analysis Method for Solving various types of Problems of Partial Differential Equations

I-Optimal designs for third degree kronecker model mixture experiments

Estimates and Forecasts of GARCH Model under Misspecified Probability Distributions: A Monte Carlo Simulation Approach

Ecological Archives E A1. Meghan A. Duffy, Spencer R. Hall, Carla E. Cáceres, and Anthony R. Ives.

Diebold, Chapter 7. Francis X. Diebold, Elements of Forecasting, 4th Edition (Mason, Ohio: Cengage Learning, 2006). Chapter 7. Characterizing Cycles

(10) (a) Derive and plot the spectrum of y. Discuss how the seasonality in the process is evident in spectrum.

Exponential Smoothing

Forecasting. Summary. Sample StatFolio: tsforecast.sgp. STATGRAPHICS Centurion Rev. 9/16/2013

Multivariate Auto-Regressive Model for Groundwater Flow Around Dam Site

APPLICATION OF HOLT-WINTERS METHOD IN WATER CONSUMPTION PREDICTION

AP Chemistry--Chapter 12: Chemical Kinetics

STAD57 Time Series Analysis. Lecture 5

Mixed-frequency VAR models with Markov-switching dynamics

WEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x

Nature Neuroscience: doi: /nn Supplementary Figure 1. Spike-count autocorrelations in time.

Methodology. -ratios are biased and that the appropriate critical values have to be increased by an amount. that depends on the sample size.

THE UNIVERSITY OF TEXAS AT AUSTIN McCombs School of Business

Robust estimation based on the first- and third-moment restrictions of the power transformation model

Lecture 15. Dummy variables, continued

Biol. 356 Lab 8. Mortality, Recruitment, and Migration Rates

Tourism forecasting using conditional volatility models

Licenciatura de ADE y Licenciatura conjunta Derecho y ADE. Hoja de ejercicios 2 PARTE A

KINEMATICS IN ONE DIMENSION

Distribution of Estimates

Financial Econometrics Jeffrey R. Russell Midterm Winter 2009 SOLUTIONS

Lecture 18 GMM:IV, Nonlinear Models

Adeeb Ahmed Ali AL Rahamneh. Applied Statistics, Faculty of Business, AL Balqa Applied University, Jordan

Fourier Series & The Fourier Transform. Joseph Fourier, our hero. Lord Kelvin on Fourier s theorem. What do we want from the Fourier Transform?

Problem set 2 for the course on. Markov chains and mixing times

Modeling and Forecasting Volatility Autoregressive Conditional Heteroskedasticity Models. Economic Forecasting Anthony Tay Slide 1

STRUCTURAL CHANGE IN TIME SERIES OF THE EXCHANGE RATES BETWEEN YEN-DOLLAR AND YEN-EURO IN

A Generalization of Student s t-distribution from the Viewpoint of Special Functions

THE WAVE EQUATION. part hand-in for week 9 b. Any dilation v(x, t) = u(λx, λt) of u(x, t) is also a solution (where λ is constant).

Oscillation Properties of a Logistic Equation with Several Delays

Chapter 3 Boundary Value Problem

1. Calibration factor

Vehicle Arrival Models : Headway

Quarterly ice cream sales are high each summer, and the series tends to repeat itself each year, so that the seasonal period is 4.

EVALUATING FORECASTING MODELS FOR UNEMPLOYMENT RATES BY GENDER IN SELECTED EUROPEAN COUNTRIES

Analyze patterns and relationships. 3. Generate two numerical patterns using AC

5.2. The Natural Logarithm. Solution

MAC1105-College Algebra

A First Course on Kinetics and Reaction Engineering. Class 19 on Unit 18

Wisconsin Unemployment Rate Forecast Revisited

BOOTSTRAP PREDICTION INTERVALS FOR TIME SERIES MODELS WITH HETROSCEDASTIC ERRORS. Department of Statistics, Islamia College, Peshawar, KP, Pakistan 2

Navneet Saini, Mayank Goyal, Vishal Bansal (2013); Term Project AML310; Indian Institute of Technology Delhi

6.2 Transforms of Derivatives and Integrals.

Chapter 7 Response of First-order RL and RC Circuits

Properties of Autocorrelated Processes Economics 30331

ALMOST UNBIASED RATIO AND PRODUCT TYPE EXPONENTIAL ESTIMATORS

A Study of Design Method of Process and Layout of Parts and Facilities for Cell Production

Section 7.4 Modeling Changing Amplitude and Midline

23.5. Half-Range Series. Introduction. Prerequisites. Learning Outcomes

EFFICIENT CLASSES OF RATIO-TYPE ESTIMATORS OF POPULATION MEAN UNDER STRATIFIED MEDIAN RANKED SET SAMPLING

Has the Business Cycle Changed? Evidence and Explanations. Appendix

Reading from Young & Freedman: For this topic, read sections 25.4 & 25.5, the introduction to chapter 26 and sections 26.1 to 26.2 & 26.4.

Linear Gaussian State Space Models

04. Kinetics of a second order reaction

Estimation Uncertainty

Lecture 23 Damped Motion

Article from. Predictive Analytics and Futurism. July 2016 Issue 13

New Oscillation Criteria For Second Order Nonlinear Differential Equations

anempirical Study Strictly as per the compliance and regulations of :

State-Space Models. Initialization, Estimation and Smoothing of the Kalman Filter

Introduction D P. r = constant discount rate, g = Gordon Model (1962): constant dividend growth rate.

Distribution of Least Squares

BRIEF NOTE ON HEAT FLOW WITH ARBITRARY HEATING RATES IN A HOLLOW CYLINDER

t + t sin t t cos t sin t. t cos t sin t dt t 2 = exp 2 log t log(t cos t sin t) = Multiplying by this factor and then integrating, we conclude that

TP A.14 The effects of cut angle, speed, and spin on object ball throw

Forecast of Adult Literacy in Sudan

Frequency independent automatic input variable selection for neural networks for forecasting

On a Discrete-In-Time Order Level Inventory Model for Items with Random Deterioration

Thus the force is proportional but opposite to the displacement away from equilibrium.

Cointegration and Implications for Forecasting

Using the correlation dimension to detect non-linear dynamics: Evidence from the Athens Stock Exchange. David Chappell University of Sheffield

V L. DT s D T s t. Figure 1: Buck-boost converter: inductor current i(t) in the continuous conduction mode.

DUALITY IN NONLINEAR FRACTIONAL PROGRAMMING PROBLEM USING FUZZY PROGRAMMING AND GENETIC ALGORITHM

Vectorautoregressive Model and Cointegration Analysis. Time Series Analysis Dr. Sevtap Kestel 1

On the approximation of particular solution of nonhomogeneous linear differential equation with Legendre series

Stationary Time Series

LAPLACE TRANSFORM AND TRANSFER FUNCTION

Oscillation of an Euler Cauchy Dynamic Equation S. Huff, G. Olumolode, N. Pennington, and A. Peterson

Transcription:

Inernaional Conference on Innovaive Applicaions in Engineering and Inforaion echnology(iciaei207) Inernaional Journal of Advanced Scienific echnologies,engineering and Manageen Sciences (IJASEMSISSN: 2454356X) Volue.3,Special Issue.,March.207 MODIFIED HOL s LINEAR MODELS FOR INRADAY DAA B.SAROJAMMA, RAMAKRISHNA REDDY 2, S.V.SUBRAHMANYAM 3, S.VENKAARAMANA REDDY 4*,S.K.GOVINDARAJULU 5,R.ABBIAH 6,2,3,5: Deparen of saisics, s.v.universiy, irupai57502. 4.Deparen of physics, s.v.universiy, iorupai57 502. * Auhor for correspondence: drsvreddy23@gail.co ABSRAC:here are any ypes of ie series odels and soe of he are univariae ie series odels, ulivariae ie series odels, inerval ie series odels and inraday ie series odels ec.. in his paper wo inraday ie series odels are inroduced and hey are odified hol s odeli and odified hol s odelii are esiaed using Roo ean square error crieria y aking alpha rages fro 0. o 0.9 ane0.99 for all hree odels i.e. hol s linear odel, odified hol s linear odeli,odified hol s linear odelii epirical invesigaion are calculaed using inraday daa of eperaure of dalles KEYWORDS: Hol s linear odel, odified Hol s linear odeli, odified Hol s linear odelii, eperaure I.INRODUCION here are so any odels are developed and odified for inraday odels. Inraday odels possesses here won odels, i can no ake usual odels which saisfies year wise daa, onhly daa and quarer daa. General odels for ie series are single exponenial soohing odel, Hol linear odel, Hol winer odel, Adopive exponenial soohing odel, Auo regressive odel, oving average odels, Auo regressive oving average odels for differen orders of Auo regressive and oving averages, Auo regressive inegraed oving averages(p, q, r) for differen values of p, q, r, differen odels of Auo regressive condiionally heeroscedasiciy like generalized Auo regressive condiional heeroscedasiciy(garch), IGARCH,EGARCH ec. hese odels are univariae odels of ie series.mulivariae odels of ie series are vecor auo regression (VAR), vecor auo regressive oving average (VARMA), vecor auo regressive inegraed oving average (VARIMA), uliple Regression, Discoun weighed regression odels ec., In his paper we explain Hol s linear odel and inroduced wo odified Hol s odels for inraday daa. Modified Hol s odel is fied y odificaion of Hol odel i.e., in place of linear rend y susiuing exponenial curve. Modified Hol s odel2 is fied y odificaion of Hol odel i.e in place of linear rend y susiuing power curve. Which odel is es aong Hol s linear odel, Hol s odified odel, Hol s odified odel2 using Roo ean square error crieria. Generally Hol s odel is ased on seasonaliy and rend. In Hol s odel rend follows addiive odel. Hol s odel is a wo paraeer odel. Hol (957) exended single exponenial soohing o linear exponenial soohing o allow forecasing of daa wih rends. Equaions for rend, level and forecas are as follows L ˆ u ( )( L ) where L denoes level a ie and i oains su of wo coponens, firs coponen is produc of consan wih ie series value Y and second coponen is su of level L and esiaed value of rend ˆ and his su is uliplied wih ( ) L is level a ie u is ie series value a ie L is level a ie poin ˆ is rend a ie poin is a consan lies eween 0 and, generally is susiued for differen values like 0., 0.2, 0.3, 0.4,,0.9 and upon using ean square error crierion we conclude which is he es sui o daa, y iniu value of MSE. Equaion for rend ( L L ) ( ) Here denoes rend a ie poin and i is su of wo coponens, firs coponen is L is suraced fro L and ha difference is uliplied wih consan β and second coponen is produc of ( ) wih. Where is rend a ie poin www.ijases.org Page 32

Inernaional Conference on Innovaive Applicaions in Engineering and Inforaion echnology(iciaei207) Inernaional Journal of Advanced Scienific echnologies,engineering and Manageen Sciences (IJASEMSISSN: 2454356X) Volue.3,Special Issue.,March.207 L is level a ie L is level a ie poin is rend a ie is consan lies eween 0 and. F L.for forecas. Hol odel assues linear for of forecas equaion and calculaion will e changed y adding one year daa. hus ˆ is an uniased esiaor of. Generally Hol s odel is used when ie series daa is in he for of year wise or onh wise where as daa is in he for of day wise or hour wise i can no sui well. herefore in his paper we are inroduced wo odified Hol s odels. Modified Hol s odel : Generally Hol s odel follows linear rend. odified rend Hol s odel follows exponenial curve of for Y L he exponenial curve used for forecas is Y L Modified Hol s odel is convered in o General Hol s odel y aking naural logarihs on oh sides. logy log L logy log L log F A B where F is forecas for odified Hol s odel. A is level for odified Hol s odel. B is rend for odified Hol s odel. he hree equaions for odified Hol s odel are as follows For level A Y ( )( A B ) For rend B ( A A ) ( ) B For Forecas Y A B where lies eween 0 and, lies eween 0 and. Modified Hol s ehod 2: In his odified odel, power curve is used in place of linear rend of Hol s odel. In general power curve is Y ax he odified Hol s ehodii is F L By aking log on oh sides, we ge log F log L log Y A B log F www.ijases.org Page 33 Y A log L B log he hree equaions for level, rend and forecas using odified Hol s odel2 are For level A Y ( )( ) 2 A 2 For rend B 2( A A ) ( 2) B For forecas F A B Here oh 2 and 2 are lies eween 0 and. Generally linear odel ay flucuae i.e., i ay ake posiive or negaive values. By aking log o any daa i soohes daa and i decreases errors. Roo Mean Square Error: Posiive square roo of ean square error gives Roo ean square error ( RMSE ). RMSE n i ( Y F) n Mean square error and Roo ean square error crieria is especially used o choose which odel possesses es fi o daa copared wih soe oher odel. A odel which akes sall MSE or RMSE is he es odel copared o oher odels. Relaive Errors: Relaive or percenage errors are copued y aking difference of original value and forecas value which gives error, his error is divided wih original value and uliplies 00. Y F PE 00 Y Mean Percenage Error ( MPE ): Su of percenage errors divided y nuer of oservaions gives Mean Percenage Error ( MPE ). Mean Asolue Percenage Error ( MAPE ): Asolue percenage error divided y oal nuer of oservaions gives ean asolue percenage error ( MAPE ) n PE n MAPE. Generally all he aove errors of accuracy are used o sudy aou consans fied o daa and o choose es odel o daa. A odel which possesses iniu error is good for daa. Epirical invesigaions: Inraday daa plays an vial role in any fields like aospheric science for forecas of hour o hour eperaure in suer, in rainy season oisure in air ec., in usiness arkes forecas of rading hour o hour, loss or gain of 2

Inernaional Conference on Innovaive Applicaions in Engineering and Inforaion echnology(iciaei207) Inernaional Journal of Advanced Scienific echnologies,engineering and Manageen Sciences (IJASEMSISSN: 2454356X) Volue.3,Special Issue.,March.207 rading ec. in elephone exchange deparen forecas of call deand of hour o hour asis, in call cener o esiae aou cell services ec. In his we are paperfied hree odels of Hol s ehod o forecas eperaure of Dallas daa. Hol s ehod: For forecas of Dallas daa we are fiing Hol s ehod. Hol s ehod conains rend, level and forecas equaions separaely level rend L ˆ u ( )( L ) ( L L ) ( ) F L forecas Where L is level a ie www.ijases.org Page 34 is rend a ie poin L is level a ie poin is rend a ie, are consans lies eween 0 and. By aking ie series value as Dallas eperaure (u ), we fi Hol linear odel for differen values of α and β as follows HOL,s MODEL CALCULAION PERIODS EMPERAURE alpha ea L alpha ea forecas when = Error Error square 52 0.9 0. 52 0 0. 0.9 52 2 52 52 7.E6 52 0 0 3 5 5. 0.09 5.0 0.0 E04 4 52 5.90 0.0009 5.900 0.0999 0.00998 5 5 5.09 0.089 5.008 0.008 6.6E05 6 5 5.0008 0.0826 50.982 0.0883 0.0067 7 50 50.098 0.653 49.9265 0.07346 0.0054 8 50 49.9927 0.587 49.834 0.660 0.02756 3393 73 65.7 6.57 72.27 0.73 0.5329 33932 74 73.827 6.7257 80.5527 6.5527 42.9379 33933 74 74.6553 6.3596 80.792 6.792 46.208 33934 72 72.879 5.34475 78.2239 6.2239 38.7365 33935 70 70.8224 4.6046 75.427 5.427 29.4522 33936 67 67.8427 3.8467 7.6889 4.6889 2.9855 33937 66 66.5689 3.3347 69.903 3.903 5.2339 33938 65 65.4903 2.8929 68.3832 3.3832.446 33939 65 65.3383 2.5884 67.9267 2.9267 8.56574 33940 65 65.2927 2.325 67.677 2.677 6.85222 3394 64 64.368.9994 66.362 2.362 5.5757 33942 64 64.236.7869 66.023 2.023 4.09262 FORECAS FOR 24 HOURS 33943 6.36363636 6.8296.36756 63.97.8335 3.3672 33944 60.304958 60.5935.072 6.7007.3965.9508 33945 59.24475524 59.4903 0.8866 60.3765.38.28087 33946 58.853469 58.4044 0.68895 59.0934 0.908 0.8246 33947 57.258743 57.3226 0.588 57.8345 0.7086 0.5026 33948 56.06643357 56.2432 0.35275 56.596 0.5296 0.28043 33949 55.0069930 55.659 0.20974 55.3756 0.3686 0.359 33950 53.94755245 54.0904 0.082 54.76 0.224 0.0509

Inernaional Conference on Innovaive Applicaions in Engineering and Inforaion echnology(iciaei207) Inernaional Journal of Advanced Scienific echnologies,engineering and Manageen Sciences (IJASEMSISSN: 2454356X) Volue.3,Special Issue.,March.207 3395 52.88889 53.065 0.0343 52.9822 0.094 0.00885 33952 5.8286733 5.944 0.38 5.8059 0.02276 0.00052 33953 50.76923077 50.8729 0.234 50.645 0.2774 0.0632 33954 49.7097902 49.803 0.353 49.4877 0.222 0.04933 33955 48.65034965 48.734 0.3906 48.3435 0.30689 0.0948 33956 47.59090909 47.6662 0.4584 47.2078 0.383 0.4677 33957 46.5346853 46.599 0.592 46.0799 0.4559 0.20394 33958 45.47202797 45.5328 0.5739 44.9589 0.535 0.26332 33959 44.425874 44.4672 0.623 43.844 0.56847 0.3236 33960 43.3534685 43.4022 0.6673 42.735 0.689 0.3826 3396 42.29370629 42.3378 0.707 4.6308 0.66287 0.4394 33962 4.23426573 4.2739 0.7427 40.532 0.70303 0.49426 33963 40.748257 40.205 0.7748 39.4357 0.7393 0.5463 33964 39.538462 39.474 0.8036 38.3438 0.7756 0.5953 33965 38.05594406 38.0847 0.8295 37.2552 0.80072 0.645 33966 36.9965035 37.0224 0.8528 36.696 0.82692 0.68379 Modified Hol s odel: Year wise, quarer wise and onh wise daa can no saisfy univariae odels of inraday and inra week daas. In his odified Hol s odel we are aking curve of for exponenial in place of rend in Hol s ehod. By akeing logarihs o exponenial curve i cover o rend. Generally log soohes daa and i reduces he flucuaions. Y L ake log on oh sides logy log L logy log L log F A B he odified Hol s odel conains level, rend and forecas equaions are For level A Y ( )( A B ) For rend B ( A A ) ( ) B For Forecas Y A B where lies eween 0 and, lies eween 0 and. Exponenial curve calculaion: Periods eperaure alpha ea Log y L B as alpha ea forecas Error square 52 0.7 0.9 3.952 3.952 0.0 4.6052 4.6057 0.3 0. 8.5564 2.20759244 2 52 3.952 5.3328.2444 0.2865 0.2865 5.554 2.5606446 3 5 3.938 4.477 0.699 0.3579 0.3579 4.7756 0.7992803 4 52 3.952 4.986 0.273 2.06 2.060 6.2596 5.32836629 5 5 3.938 4.630 0.402 0.934 0.9338 5.5435 2.597597689 6 5 3.938 4.453 0.532.8759.87592 6.293 5.56693942 7 50 3.92 4.6258 0.2047.586.58605 6.28 5.28979507 8 50 3.92 4.602 0.00 6.9388 6.93885.54 58.9849382..... 3393 73 4.2905 3.0033 2.703 0.99436 0.99436 3.9977 0.0857987 33932 74 4.304 4.22.3582 0.3069 0.3069 4.583 0.04594729 33933 74 4.304 4.3683 0.2764.2859.28589 5.6542.822979608 33934 72 4.2767 4.6899 0.37.486.4863 5.8386 2.4395289 www.ijases.org Page 35

Inernaional Conference on Innovaive Applicaions in Engineering and Inforaion echnology(iciaei207) Inernaional Journal of Advanced Scienific echnologies,engineering and Manageen Sciences (IJASEMSISSN: 2454356X) Volue.3,Special Issue.,March.207 33935 70 4.2485 4.7255 0.0637 2.7532 2.7535 7.4787 0.4340235 33936 67 4.2047 5.869 0.426 0.8637 0.86369 6.0506 3.407270548 33937 66 4.897 4.7479 0.3529.046.0457 5.7895 2.55950689 33938 65 4.744 4.6589 0.0448 3.052 3.056 7.764 2.88588233 33939 65 4.744 5.253 0.5376 0.6206 0.6206 5.879 2.8855860 33940 65 4.744 4.6836 0.457 0.7828 0.7828 5.4664.66939709 3394 64 4.589 4.55 0.0735 2.60 2.6006 7.62 9.03949884 33942 64 4.589 5.0596 0.4649 0.7658 0.76585 5.8254 2.777365797 Forecas for 24 hours: 33943 6.3636364 4.68 4.6294 0.3407.0768.07685 5.7062 2.526284346 33944 60.304958 4.0994 4.585 0.009 4.703 4.7028 9.2827 26.86694988 33945 59.2447552 4.087 5.642 0.9554 0.0456 0.04563 5.6876 2.57907823 33946 58.85347 4.0636 4.5508 0.8865 0.205 0.2047 4.673 0.369254389 33947 57.25874 4.0453 4.233 0.973.6229.62285 5.8559 3.278502745 33948 56.0664336 4.0265 4.5754 0.3278.54.539 5.6907 2.769565602 33949 55.006993 4.0075 4.524 0.0238 3.7364 3.73644 8.2489 7.98966377 33950 53.9475524 3.988 5.2663 0.6808 0.3844 0.38444 5.6507 2.76458092 3395 52.8889 3.9682 4.4729 0.6459 0.437 0.43708 4.9 0.88707274 33952 5.828673 3.9479 4.2366 0.48.9096.90958 6.46 4.83208225 33953 50.7692308 3.9273 4.5929 0.3356.092.0997 5.6849 3.089242984 33954 49.7097902 3.9062 4.4398 0.043 2.2608 2.26085 6.7007 7.809020308 33955 48.6503497 3.8847 4.7295 0.27.3052.30524 6.0347 4.62269335 33956 47.590909 3.8626 4.543 0.666.7923.79234 6.3066 5.97294626 33957 46.534685 3.840 4.580 0.0759 2.5785 2.57852 7.586.026463 33958 45.472028 3.87 4.895 0.223.500.50007 6.396 6.262590979 33959 44.425874 3.7935 4.554 0.29.584.584 6.0697 5.8953 33960 43.353469 3.7694 4.4595 0.0608 2.8007 2.80068 7.2602 2.856243 3396 42.2937063 3.7446 4.7993 0.39.65.6506 5.9644 4.9274479 33962 4.2342657 3.793 4.3928 0.3347.0946.09463 5.4874 3.26397 33963 40.748252 3.6932 4.235 0.7 2.99 2.992 6.4234 7.45386828 33964 39.53846 3.6665 4.4936 0.247.3982.3986 5.897 4.95664665 33965 38.055944 3.639 4.349 0.36.994.99404 6.3089 7.2808482 33966 36.9965035 3.608 4.4202 0.085 2.224 2.2238 6.646 9.85794833 www.ijases.org Page 36

alpha ea Inernaional Conference on Innovaive Applicaions in Engineering and Inforaion echnology(iciaei207) Inernaional Journal of Advanced Scienific echnologies,engineering and Manageen Sciences (IJASEMSISSN: 2454356X) Volue.3,Special Issue.,March.207 Modified Hol s odel 2: Hol s linear odel forecas follows linear odel. In his odified Hol s odel2 we are assuing ha forecas follows power curve of for Y ax he forecas equaion of odified Hol s odel 2 is F L By aking log on oh sides, we ge log F log L log Y A B log F, log WhereY A log, L B, he hree equaions for level, rend and forecas are as follows For level A Y ( )( ) 2 A 2 For rend B 2( A A ) ( 2) B For forecas Y A B α and β are consans lies eween 0 and. Power curve calculaion forecas when = ERROR error square Period alpha ea logy L B 0.9 0.9 0 0 0.6935 0. 0. 2 0.6935 0.6935 0.6935 0.6935 0 0 3.0986.2738 0.4602.38629 0.28768 0.08276 4.38629.40642 0.2974.5875 0.202 0.04049 5.60944.6885 0.2209.70356 0.0942 0.00886 6.7976.79656 0.8203.83976 0.048 0.0023 7.9459.9498 0.5556.97859 0.03268 0.0007 3393 0.432 9.38888 8.44999 0 0.43208 08.828 33932 0.432.728 2.45052 7.8389 7.40675 54.86 33933 0.432 0.753 0.343 3.6233 3.97 0.835 33934 0.4322 0.4506 0.284 0.669 0.8476 0.0344 33935 0.4322 0.4056 0.0689 0.667 0.265535 0.0705 33936 0.4322 0.4227 0.00844 0.3368 0.095482 0.0092 33937 0.4323 0.432 0.00936 0.43 0.0036.3E06 33938 0.4323 0.4332 0.0089 0.445 0.00922 8.5E05 33939 0.4323 0.4326 0.0004 0.435 0.00279 7.8E06 33940 0.4323 0.4323 0.0003 0.4322 0.0004.3E08 3394 0.4324 0.4323 2E05 0.432 0.00032 9.7E08 33942 0.4324 0.4324 4.6E05 0.4323 7.9E05 6.2E09 forecas for 24 hours 33943 0.4324 0.4324 3.9E05 0.4324 8.3E06 6.8E 33944 0.4325 0.4325 3.E05 0.4325 E05.E0 33945 0.4325 0.4325 2.9E05 0.4325 2.2E06 4.7E2 33946 0.4325 0.4325 2.9E05 0.4325 4.02E07.6E3 33947 0.4326 0.4326 2.9E05 0.4326 3.32E07.E3 www.ijases.org Page 37

Inernaional Conference on Innovaive Applicaions in Engineering and Inforaion echnology(iciaei207) Inernaional Journal of Advanced Scienific echnologies,engineering and Manageen Sciences (IJASEMSISSN: 2454356X) Volue.3,Special Issue.,March.207 33948 0.4326 0.4326 2.9E05 0.4326 5.52E08 3E5 33949 0.4326 0.4326 2.9E05 0.4326.8E08 3.3E6 33950 0.4326 0.4326 2.9E05 0.4326.2E08.4E6 3395 0.4327 0.4327 2.9E05 0.4327 2.4E09 5.9E8 33952 0.4327 0.4327 2.9E05 0.4327 4.E0.7E9 33953 0.4327 0.4327 2.9E05 0.4327 7.4E0 5.5E9 33954 0.4328 0.4328 2.9E05 0.4328 E09.E8 33955 0.4328 0.4328 2.9E05 0.4328.E09.2E8 33956 0.4328 0.4328 2.9E05 0.4328.E09.2E8 33957 0.4329 0.4329 2.9E05 0.4329.E09.E8 33958 0.4329 0.4329 2.9E05 0.4329.E09.E8 33959 0.4329 0.4329 2.9E05 0.4329.E09.E8 33960 0.4329 0.4329 2.9E05 0.4329.E09.E8 3396 0.433 0.433 2.9E05 0.433.E09.E8 33962 0.433 0.433 2.9E05 0.433.E09.E8 33963 0.433 0.433 2.9E05 0.433.E09.E8 33964 0.433 0.433 2.9E05 0.433.E09.E8 33965 0.433 0.433 2.9E05 0.433.E09.E8 33966 0.433 0.433 2.9E05 0.433.E09.E8 Y A B SUMMARY AND CONCLUSIONS In his paper we inroduced wo odified Hol s linear odels for inraday daa. Modified Hol s odel: Year wise, quarer wise and onh wise daa can no saisfy univariae odels of inraday and inra week daas. In his odified Hol s odel we are aking curve of for exponenial in place of rend in Hol s ehod. By akeing logarihs o exponenial curve i cover o rend. Generally log soohes daa and i reduces he flucuaions. Y L ake log on oh sides logy log L logy log L log F A B he odified Hol s odel conains level, rend and forecas equaions are For level A Y ( )( A B ) For rend B ( A A ) ( ) B For Forecas Y A B where lies eween 0 and, lies eween 0 and. Modified Hol s odel 2: Hol s linear odel forecas follows linear odel. In his odified Hol s odel2 we are assuing ha forecas follows power curve of for Y ax he forecas equaion of odified Hol s odel 2 is F L By aking log on oh sides, we ge log F log L log log F WhereY, A log L B, log www.ijases.org Page 38, he hree equaions for level, rend and forecas are as follows For level A Y ( )( ) 2 A 2 For rend B 2( A A ) ( 2) B For forecas α and β are consans lies eween 0 and. hese odels are epirically calculaed using inraday daa of Dallas and 24 hours forecas is given. Biliography [] Gould, P.G., Koehler, A.B., synder, R.D., Hyndan, R.J& Vahid Araghi,(2008).Forecasing ie series wih uliple season paern European journal of operaional Research, 9, 207222. [2] Harvey, A. & koopan, s.j.(993). Forecasing hourly elecriciy deand using ievarying splines, journal of he Aerican saisical associaion, 88, 228236. [3] Jaes w aylor 200. Exponenially ehods for forecasing inraday ie series wih uliple seasonal cycle. Inernaional journal of forecasing 26, 627646. [4] Porier, D.J. (973). Piece wise regression using cuic splines, journal of he Aerican saisical Associaion, 68, 55524. [5] Spyros Makridakis, seven C. wheelwrighr, Ro J.hyndan. forecasing ehods and Applicaions, 3 rd Ed., John wiley & sons.

2024 © sciencedocbox.com Privacy Policy | Terms of Service | Feedback