Various Types of Time Series Analysis - Essay Example

?Time Series Analysis There are two types of analysis schemes, ly the qualitative analysis technique and the quantitative mode of analysis technique. Each of them has its own strengths and weaknesses, and they have a vast field under them. Time series analysis is an element of the same process and belongs to the quantitative mode of analysis. In the time series analysis, various other tools and techniques are available that make it a powerful tool in itself for the analytical processes that are quantitative in nature. As the name implies, this form of observation is based on gathering various items monitored constantly and through repetitive measurements. The measurement is based on a proper sequence, and time intervals are equally distant and uniform (Schelter, Winterhalder et al. 319). The main aim of this kind of analysis is to determine any possible existence of a pattern or sequence in a given set of data. The time series analysis itself offers variety of methods, namely the forecasting approach, the univariate approach, which involves limited variables, and other advanced techniques like Gaussian and Box-Jenkins model. Large number of events can be counted as examples of time series analysis that we see in our daily life in our routine activities. For example, the constant rise in the inflation rate, the unemployment rate, the rise in salary, local currency depreciation, annual budgets estimation and comparison with the past values and prediction of upcoming budgets – all these things are possible through the effective tool known as time series analysis. Time series analysis is a vast entity in itself and contains various other methods and approaches, which makes it one of the most effective means of quantitative analysis of data. Various types of Time Series Analysis Continuous time series As the name applies, the samples and patterns are collected over a continuous and recurrent time frame (Tsay 287). Discrete In contrast to continuous time series, the discrete method attains certain values at fixed and definitive moments. Deterministic vs. Stochastic The data so obtained is deterministic in nature, that is, the accuracy and predication level is relatively high and accurate. The stochastic method involves relative use of probability and assumption based on the trends. These trends are collected from the past and present values, which enables the prediction of future trends. Advantages There are a number of advantages attached to this form of analysis; the first and foremost is the possibility to analyze things based on solid foundations and evidence, which involves study and consideration of samples and patterns from past values and may include the data from present values if a future trend is to be determined. It enables gathering data on a more consistent pattern that is relatively more reliable. Another advantage of this pattern is the co-relational factor and dependency between the variables involved. With the element of dependency in the analysis, the results become more reliable and consistent, and in such cases a change in one, or any other alteration, might result in disturbance and variation in the other, so the entire system is under a uniform control and each entity is dependent on the presence and behavior of the other entity in the system under analysis. Due to this feature, it has the ability to determine the linear and non-linear functions and relations. Other salient features of time series analysis include constant observation, with no data missing in-between, and the time slots and observational chunks are equally spaced. Applications Though time series analysis finds its application in a large number of places and circumstances, the most notable of them is the process of forecasting. Forecasting is an essential tool of managerial world and in other processes where predictions are needed and made about a certain future value. Time series analysis is the best tool for it. The process is naturally designed in such a way that completely fulfils the requirements of a forecasting method. Forecasting as an essential tool of management field Forecasting a trend, pattern or activity is an integral part of any business endeavor undertaken. Forecasting application ranges from small enterprises to large economic setups, as well the governmental schemes and annual budgets and audits. Forecasting can make life easy in that regard and enable valuable estimations about the future trends in the context of profits and other essential values. With the help of time series analysis, other methods and mechanisms can be used for the purpose of estimation and prediction. Few of these methods are as follows. Moving Average In this approach, each variable bears a considerable weight age, and while it is clear from the name that averages are determined, the respective variable has its own weight age which affects the result directly. It is represented by a given equation derived from various variables involved. Though it is relatively easy, it is still efficient enough for the purpose of forecast determination. Regression analysis The regression analysis comes in both simple and multiple regression patterns and are effective tools of forecasting and value prediction. Regression analysis enables establishing relationship between two or more variables that constitute the respective system. Responses are observed and obtained over a regular interval of time to develop a constant value. The linear regression model, as the name implies, yields a straight line. Various elements are plotted against each other on x- axis and y-axis respectively, and their values are compared at different and constant intervals (Kleinbaum 3). More elaborative means can also be applied in terms of forecasting, which primarily includes methods like Box-Jenkins methodology. A relatively simple method of forecasting often used in short-term measures includes a self-projection approach, which is relatively low on accuracy and end yield but is useful in cases where resources are relatively constrained and results are required in a shorter span of time. Another weakness in the self-projection approach is the fact that estimations are loosely based on prediction rather than any concrete sequence or pattern obtained through solid evidence and experiment. The scope of this kind of forecasting method is limited to a certain number of variables and components and does not take into account all variables and external components, which may be a deciding factor in determining the output of a given product or pattern. Inside the self-projection model, the modes which are usually applied include seasonal model schemes, and decomposition models approaches, which in themselves are relatively simple in nature and limited in capacity. The rudimentary form of forecasting and time analysis techniques are more specifically based on the trial and error approach or utilization of limited resources. These were in practice when the other accurate and relatively more reliable systems were not in commercial practice. Such methods compromise relatively over the end yield, and the result of forecasted value so obtained might be slightly compromising and deviant from the values desired or the actual existing values. ARIMA Model Scheme ARIMA is acronym for Auto Regressive Integrated Moving Average scheme. It is relatively more effective and robust in its application and has a larger scope compared to the other elementary modes of forecasting and value prediction. It takes into account relatively greater number of variables, inputs, outputs and other elements which add value to the end result and make the forecasting relatively more reliable and desired. It is beneficial and effective for the reason that it allows a wider scope of time series analysis patterns. Stochastic model approach comes under category of this model of forecasting scheme (Segura and Braun 33). ARMIA is also called the Box-Jenkins model. Such models are designated purely for the purpose of economic forecasts and values estimations. Their scope is relatively larger and promises better and effective results. Its capability range rotates between the univariate transfer function and the multivariate transfer function. Another advantage of the Box-Jenkins approach is the isolation and identification of the disturbances and other factors hampering the entire process of forecasting. It enables identification of those entities which are non-value in the end result. This is made possible through the usage of control equation. Control equation allows highlighting and evaluating all those factors which are non-entity or disturbances. Identification of such elements is of high value since they have a direct negative impact on the entire output. Their isolation can help achieve results that are more accurate and near to the realistic values. While different methods of forecasting are used, one of them is that of causal relationship, that is, the cause and effect of different variables and entities involved in a system. For example, in the case of a business process, the elements or processes which contribute to the making of final product have a direct impact on the items which will be produced through these constituents. This serves as an example of cause and effect relationship. Working mechanism of the Box-Jenkins model approach Various steps are involved in the Box-Jenkins model scheme. These processes work in a closed loop form setup, and one process complements another. Starting from the top, the first element of the process is the identification of the model. A pre-requisite to the Box-Jenkins process is the stationary nature of the variables and the entire process. Though complete stable system and variables are hard to obtain, the elements with minimal variation yield more accurate results and values. Hence, the working mechanisms of the incumbent process are largely subject to a stable and stationary element system. In many cases, the hypothetical assumption of equilibrium between the elements and function elements is assumed. The time period is relatively constant in this case. For highly accurate value estimation, a strictly stationary function system is desired (Zellner and Palm 67). This can be done either in form of the auto co-relation activity or through the partial method of auto co-relation. Once the model and its pattern are identified, the estimation follows. At this stage, the conditionality check is applied, determining the adequacy of the model and its components; this step is primarily undertaken for the purpose of minimizing the errors that might be present in the system through the method of sum of square error approach; on completion of this process, if the system and model itself are void of errors, forecasting of a given set of data is conducted; however, if there are deviations and shortcomings in the model and its components, then instead of forecasting, the model will see modification and alteration. The process is generated from the beginning, once again starting with the identification model. Apart from forecasting, the transfer function success is directly subject to input and output given to present and past values. The transfer function itself is the relationship between the input invested and the output yielded. In many cases, the output is a future value, which cannot be determined. In such cases, the future value can only be predicted, and that is possible through time series analysis. Time series analysis enables point-by-point and instantaneous comparison of different entities at different periods, which indirectly enables knowing the future value and hence the entire transfer function. Transfer functions find a large number of usages in industrial environment, where large number of products and services are in direct contact with customers, and for this reason knowing the output prior to market delivery is very vital. That is why time series analysis is a strong and suitable tool in this regard, which most suitably solves the issue of futurist value determination. The Gaussian process is a subset to the Box-Jenkins process. This process enables generation of the multivariate distribution function in the name of Gaussian process (Brockwell and Davis 546). With the help of this kind of analysis, various other possibilities appear such as spectral analysis, intervention-based analysis and, the most important and common kind, the forecasting. Another application of notable mention is that of feedback, where the input and output are in a closed system. Time series analysis is the best tool for it provides necessary information about the behavior of a particular variable and pattern inside the entire system. Spectral analysis: the components are measured and analyzed with regard to a certain spectrum and a continuous pattern. Usually some variables are tested against various time slots; however, if a single variable is in use, time series analysis is termed as the single time series. The time series analysis is a vast field in itself and contains a large number of variables and components within. These components can be horizontal, cyclic, or seasonal. Horizontal component: in this case, the given data and the particular pattern rotate and fluctuate around a fixed given value along the respective index. Seasonal component: In this case, the factors that are seasonal in nature have an impact on the respective component. Time series analysis is a powerful tool of quantitative nature; the process of forecasting is of high value in the entire business world and in economic factors. The predictions and future values, trends and expectations are largely subject to the principles and methods of forecasting. The consistent observational function and periodic idiosyncrasy make it one of the largely used tools across the world in different paradigms. Works Cited Brockwell, Peter J., and Richard A. Davis. Time Series: Theory and Methods. Springer, 2009. Print. Kleinbaum, David G. Applied Regression Analysis and Other Multivariable Methods. Cengage Learning, 2007. Print. Schelter, Bjorn, Matthias Winterhalder, and Jens Timmer. Handbook of Time Series Analysis. John Wiley & Sons, 2006. Print. Segura, Julio, and Carlos Rodriguez Braun. An Eponymous Dictionary Of Economics: A Guide To Laws And Theorems Named After Economists. Edward Elgar Publishing, 2004. Print. Tsay, Ruey S. Analysis of Financial Time Series. John Wiley & Sons, 2010. Print. Zellner, Arnold, and Franz C. Palm. The Structural Econometric Time Series Analysis Approach. Cambridge University Press, 2004. Print. Read More