The Times Series Analysis Methods and Weaknesses Using This Particular Analysis - Example

Time series Analysis (Name of the student) (Name of the institution) (Date of submission) Table of Contents Table of Contents 2 Executive Summary 3 1.0 Introduction 3 3.0 Practical application of the model 5 3.2 Box- Jenkins Methodology 7 4.0 Limitations of time series analysis 11 Bibliography 12 Appendices 13 Appendix 1: Forecasting table 13 Appendix II 14 Autocorrelations 14 Executive Summary Time series can be defined as the collection of quantitative observations which are spaced evenly over time period and are being measured successively. Time series analysis is useful in identifying seasonal variations that are very important in planning process at different times of the year. From the example of oil demand given, various governments can use time series analysis to establish the fuel demand in the country hence avoiding shortages of product which can lead to price increase. Time series analysis is reasonably accurate in the short term given that the firm is operating in a stable environments compared to other methods of estimations. In oil industry, demand for oil is very high and there is need for the companies producing oil to be up to date with changing market demand so that they can respond to oil demand in time. One of the key competitive strength of a good company is aggressive supply chain management. The paper discussed the times series analysis methods and weaknesses using this particular analysis 1.0 Introduction Time series can be defined as the collection of quantitative observations which are spaced evenly over time period and are being measured successively (Durbin & Koopman 2012). Time series analysis descriptively aimed at identifying patterns in a correlated data and giving the seasonal variation. It helps in understanding and modeling of the data, giving prediction of short and long term trends in a given issues. Time series analysis is done to help in understanding underlying structures and functions of the produced observation. This paper discusses application of time series data in solving the supply chain problem. The study uses data from the world oil consumption to discuss how the problem of demand shortage of fuel can be eliminated using data from the past forty years to estimate demand forecast in the future. The paper gives the benefits of time series, and the limitation, giving how the limitations can be overcome. 2.0 Merits of time series analysis Extensive literature researches have failed to show a clear cut winner among the various methods of time series analysis. Different types of time series requires different types of treatments. Time series methods helps in identifying some of the historical patterns using time based point of referencing. This method has made the work of observation more simplifies in the calculation in the part of time and gives it easy for various types of simulations to be done. It is so easy to use and it is more direct compared to other methods (Montgomery, Jennings & Kulahci 2011). One of the main properties of time series analysis is autocorrelation function and partial autocorrelation function. Autocorrelation function can be defined as the standard part of covariance function. Partial autocorrelation on the other hand expresses the relationship between two variables in the analysis (Durbin & Koopman 2012). Time series analysis is useful in identifying seasonal variations that are very important in planning process at different times of the year. From the example of oil demand given, various governments can use time series analysis to establish the fuel demand in the country hence avoiding shortages of product which can lead to price increase. Time series analysis is reasonably accurate in the short term given that the firm is operating in a stable environments compared to other methods of estimations (Durbin & Koopman 2012). Using time series analysis, the line of best fit can be easily drawn quite correctly in varying position a quality other methods of analysis like regression most often do lack. The desire to give description of the data over a given time period is another important factor that explains why time series analysis is being done. It allows one to have deeper understanding of a particular given data and explore future happening using past trends (Montgomery, Jennings & Kulahci 2011). It is a powerful means of studying communication process. It allows the researchers to avoid pitfall of studying communication related phenomenal in isolation. In this case, procurement and logistics of oil is being studied over a long time hence, the researcher can use past data and compare it with current happening (Ling, McAleer & Tong, 2015). Since time series uses past data, the data are readily available hence help in time management when it comes to data collection for analysis. Time series analysis is also very useful when it comes to comparing two or more communication processes and in estimating effect that these different processes have on a particular outcome (Montgomery, Jennings & Kulahci 2011). 3.0 Practical application of the model Demand planning is one of the key functions of supply chain management. This paper aimed at highlighting some of the needs for forecasting in supply chain management, giving statistical time series models for short term forecast and help in demand forecasts. Supply chain planning in most cases starts with forecasting where supplies are being match with the demand. For every firm, matching suppliers and demand is in the heart of their operations. Forecast is important taking into consideration that production systems does not instantly respond to consumer demand. Therefore, an estimation of future demand is necessary so that an efficient and effective operational plan can be made (Kirchgässner, Wolters & Hassler 2012). Resource allocation in the firms starts with forecasting; therefore it forms a central part in the management system. The finance department needs to have full understanding of the forecasting process. The marketing departments have responsibility to know how to allocate resources for various product groups and marketing campaigns. Labor requirements need to understand basic forecasting techniques to help in determine labor allocation. Other sectors need to understand the market trends and this can be better done using forecasting technique. Forecasting should be done basically for end item demand; the management is using forecasting techniques to help in making decisions to market trends (Kirchgässner, Wolters & Hassler 2012).  Time series mode is one of the most popular methods used in forecasting. The model uses past data to predict future demand of the product. It is good for products which are ordered continuously. It assumed each observed each demand data point and systematic component and random component. The demand of oil in the world is one of the most unpredictable and the supply chain needs to find how this can be fixed. With changes in consumer demand and increase in market competition combined with continuous changes in environment, companies are demanded to improve their operations (Kirchgässner, Wolters & Hassler 2012). In oil industry, demand for oil is very high and there is need for the companies producing oil to be up to date with changing market demand so that they can respond to oil demand in time. One of the key competitive strength of a good company is aggressive supply chain management. Moving average is one of the simple methods which can be used to estimate the demand of a product in the market. The graph below explains the moving average of the oil demand in European regions (Durbin & Koopman 2012). After calculating the moving average, to ensure that the forecast is more accurate, it is important to calculate mean absolute deviation. The mean absolute deviation is one of the simple assessments of demand pattern variance. Figure 1: moving average From excel, forecast is indicated by a moving average of the oil demand in the European market. From the calculation, the operation officers can easily estimate the demand of the next period. Appendix 1 gives demand forecast which can be used by the supply department in estimating the future oil demand. 3.2 Box- Jenkins Methodology This is one of the methodologies which came into limelight in 1970, by Georg Box Jenkins. The technique is based on ARIMA model and is used to solve the supply chain problem. The model integrates autogressive moving average model and also integrates components that gives the analyst to run a model with non stationery time series (Durbin & Koopman 2012). According to the author, time series is a sequence of random variable value which shows that time series have a stochastic and random property (Durbin & Koopman 2012). There are five steps in calculating the model. They include; Data preparation where in this case is the data of oil demand in Europe for the past 41 years since 1972 to 20013. Model identification: The optimal modeling type of the modeling time series is chosen at this point. In this case, we have done MA and ARMA used in demand modeling Estimating of model parameters: Using the suitable method is estimated numerical value of model parameters and we can test statistical significance of model parameters In Application the figure below explains the forecasting of the annual demand of the oil in European countries The graph has identified seasonality by autocorrelation function in remembered time series of the annual demand of the oil. As much as the time series shows annual dates so the seasonal periods are forty-one. The demand can be used forecasted using the probability in the Tukey hamming. This will help the supply department to plan for future demand. From the above figure, autocorrelation coefficient is much beyond bounds of statistical significance which has been supported and is seasonaliy with a length of Sixteen Oil_ demand Trend prediction Using ARIMA, time series can compute trend prediction using complex linear model. The figure below shows oil demand prediction over time. 4.0 Limitations of time series analysis Time series analysis is considered by most scholars as long winded and complex analysis process more so when the data has used a four period moving average. This only requires experts in statistic field to interpret and analyze. Many scholars like Chatfield (2013) have argued that historical data is not always good indication of what might happen in the future. This further gives another weakness as it is not therefore, useful in long term prediction (Granger & Newbold 2014). One way of handling the limitations of time series data is to use alternative method to come with the expected result. Regression is one sure way to estimate the relationship between phenomenons, hence it can be used. On the use of past data, the analysis can use more recent data and ascertain the source of the data to be sure of the data accuracy (Scargle et al., 2013). Bibliography Chatfield, C. 2013 the analysis of time series: an introduction. CRC press. Durbin, J., & Koopman, S. 2012 Time series analysis by state space methods (No. 38). Oxford University Press. Granger, C. & Newbold, P. 2014. Forecasting economic time series. Academic Press. Kirchgässner, G., Wolters, J., & Hassler, U. 2012 Introduction to modern time series analysis. Springer Science & Business Media. Ling, S., McAleer, M., & Tong, H. 2015 Frontiers in Time Series and Financial Econometrics (No. EI 2015-07). Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute. Montgomery, D., Jennings, C., & Kulahci, M. 2011 Introduction to time series analysis and forecasting (Vol. 526). John Wiley & Sons. Scargle, J., Norris, J., Jackson, B., & Chiang, J. 2013 Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations. The Astrophysical Journal, 764(2), 167. Appendices Appendix 1: Forecasting table Ft At - Ft (At - Ft)2 |At - Ft| Year Oil demand Forecasting Error Error Absolute RSFE MAD(t) TS(t) 1972 14993 Squared Deviation 1973 16124 1974 15192 1975 14706 1976 15675 1977 15592 15380 212 44931 212 -2228 789 -3 1978 16352 15607 745 555671 745 -2440 854 -3 1979 16745 15711 1035 1070397 1035 -3186 867 -4 1980 15619 15782 -163 26450 163 -4220 843 -5 1981 14650 15772 -1122 1258586 1122 -4058 957 -4 1982 14005 15494 -1489 2216947 1489 -2936 924 -3 1983 13738 15185 -1447 2093087 1447 -1447 782 -2 1984 13850 14768 -918 842937 918 -2365 561 -4 1985 13730 14266 -535 286413 535 -2900 382 -8 1986 14270 14041 229 52607 229 -2671 229 -12 1987 14380 13996 385 148026 385 -2286 307 -7 1988 14576 14091 485 235691 485 -1800 367 -5 1989 14605 14235 369 136478 369 -1431 367 -4 1990 14777 14390 387 149974 387 -1044 371 -3 1991 14731 14557 175 30516 175 -869 338 -3 1992 14888 14660 229 52280 229 -640 323 -2 1993 14845 14737 108 11698 108 -532 296 -2 1994 14912 14793 119 14188 119 -413 276 -1 1995 15248 14901 348 120970 348 -65 283 0 1996 15575 15034 542 293633 542 477 307 2 1997 15790 15210 580 336134 580 1056 330 3 1998 16047 15403 644 414391 644 1700 354 5 1999 15949 15587 362 130855 362 2062 354 6 2000 15804 15736 69 4729 69 2131 335 6 2001 16057 15870 187 34895 187 2317 326 7 2002 15978 15937 41 1648 41 2358 309 8 2003 16073 15985 89 7884 89 2447 297 8 2004 16222 16014 208 43419 208 2655 292 9 2005 16358 16082 276 75922 276 2931 292 10 2006 16414 16184 230 52867 230 3161 289 11 2007 16089 16189 -100 9991 100 3061 280 11 2008 15973 16188 -216 46475 216 2845 277 10 2009 15294 16058 -765 584537 765 2080 298 7 2010 15104 15872 -768 590073 768 1312 316 4 2011 14716 15598 -882 778193 882 430 338 1 2012 14203 15230 -1027 1054576 1027 -597 364 -2 2013 14086 14896 -810 655509 810 -1406 380 -4 -2188 14463576 18293 Appendix II Autocorrelations Series: Oi_demand Lag Autocorrelation Std. Errora Box-Ljung Statistic Value df Sig.b 1 .154 .151 1.042 1 .307 2 .011 .149 1.048 2 .592 3 .112 .147 1.626 3 .654 4 -.310 .145 6.206 4 .184 5 -.062 .143 6.394 5 .270 6 .055 .141 6.548 6 .365 7 -.058 .139 6.722 7 .458 8 .002 .137 6.722 8 .567 9 -.048 .135 6.847 9 .653 10 .038 .133 6.930 10 .732 11 -.003 .130 6.931 11 .805 12 -.090 .128 7.428 12 .828 13 -.020 .126 7.453 13 .877 14 -.109 .124 8.227 14 .877 15 -.124 .121 9.268 15 .863 16 -.094 .119 9.897 16 .872 a. The underlying process assumed is independence (white noise). CCF Output Created 22-MAY-2015 07:36:31 Comments Input Active Dataset DataSet1 Filter Weight Split File N of Rows in Working Data File 42 Date Missing Value Handling Cases Used For a given time series variable, cases with missing values are not used in the analysis. Also, cases with negative or zero values are not used, if the log transform is requested. Syntax CCF /VARIABLES=Oi_demand Year /LN /DIFF=1 /MXCROSS 7. Resources Processor Time 00:00:00.23 Elapsed Time 00:00:00.22 Use From First observation To Last observation Time Series Settings (TSET) Amount of Output PRINT = DEFAULT Saving New Variables NEWVAR = CURRENT Maximum Number of Lags in Autocorrelation or Partial Autocorrelation Plots MXAUTO = 16 Maximum Number of Lags Per Cross-Correlation Plots MXCROSS = 7 Maximum Number of New Variables Generated Per Procedure MXNEWVAR = 60 Notes Time Series Settings (TSET) Maximum Number of New Cases Per Procedure MXPREDICT = 1000 Treatment of User-Missing Values MISSING = EXCLUDE Confidence Interval Percentage Value CIN = 95 Tolerance for Entering Variables in Regression Equations TOLER = .0001 Maximum Iterative Parameter Change CNVERGE = .001 Method of Calculating Std. Errors for Autocorrelations ACFSE = IND Length of Seasonal Period Unspecified Variable Whose Values Label Observations in Plots Unspecified Equations Include CONSTANT [DataSet1] Model Description Model Name MOD_4 Series Name 1 Oi_demand 2 Year Transformation Natural logarithm Non-Seasonal Differencing 1 Seasonal Differencing 0 Length of Seasonal Period No periodicity Range of Lags From -7 To 7 Display and Plot All lags Applying the model specifications from MOD_4 Case Processing Summary Series Length 42 Number of Excluded Cases Due to Negative or Zero Value Before Log Transform 0 User-Missing Value 0 System-Missing Value 0 Number of Valid Cases 42 Number of Computable Zero-Order Correlations After Differencing 41 Oi_demand with Year Cross Correlations Series Pair: Oi_demand with Year Lag Cross Correlation Std. Errora -7 -.063 .171 -6 -.019 .169 -5 .055 .167 -4 .053 .164 -3 .147 .162 -2 .103 .160 -1 .024 .158 0 .132 .156 1 .122 .158 2 .073 .160 3 .034 .162 4 .014 .164 5 -.051 .167 6 -.068 .169 7 -.103 .171 Read More