Free Essay

Time Series Analysis

In: Business and Management

Submitted By fawazmry
Words 1324
Pages 6
DEPARTMENT OF MANAGEMENT STUDIES, NIT TRICHY

AN ASSIGNMENT ON

TIME SERIES ANALYSIS
PLANNING AND CONTROL OF OPERATONS

FAWAZ MOHAMED KUTTY 215112035 MBA Ist YEAR

TIME SERIES ANALYSIS
A time series may be defined as a set of values of a variable collected and recorded in a chronological order of the time intervals. Time series is used by statisticians to describe the flow of economic activity. In short time series refers to the data depending on time. It refers to a set of observations concerning any activity against different periods of time. The duration of the time period may be hourly, daily, weekly, monthly or yearly. According to Morris Hamburg “A time series is a set of statistical observations arranged in chronological order”. Therefore time series is also called historical data or historical series. The study of movement of quantitative data through time is referred to as ‘time series analysis’. Time series is of great importance to the planners of economic development and economists. The success of planning depends upon making accurate forecasts of future conditions of economy. It enables the economists to foresee what is likely to come and to analyze the repercussions of past behavior. The analysis of time series enables us to understand the past behavior or performance. Time series analysis can be used to know how the data changes over time and find out probable reasons for such change.

UTILITY OF TIME SERIES ANALYSIS
Analysis of time series is of relevance whenever a variable is found to vary over time. Variable such as Sales, Production, Profit, Population and Employment opportunity assume different values at different points of time. The importance is given in the following points 1. Analysis of time series helps to know the past conditions: The observations made on the past few periods help to know the conditions properly 2. In assessing the present achievements 3. In predicting the future: on the basis of the past and the present conditions, the future is well predicted. It helps to forecast scientifically. 4. In comparison: various time series could be compared with regard to their movement over a long period and vital inferences could be drawn. 5. In forewarning: as it predicts the future, good or bad, eventualities could be met with the necessary preparedness. Losses if any, could be minimized, profits, if any could be increased.

COMPONENTS OF TIME SERIES
A Time series may contain one or more of the following four components: 1. 2. 3. 4. Secular trend Seasonal variation Cyclical variation Irregular variation

It is ordinarily assumed that there is a multiplicative relationship amongst these four components. Mathematically it can be written as Y=TxSxCxI Where, T= trend, S= seasonal variation, C= cyclical variation, I=irregular variation. SECULAR TREND These are the changes that have occurred as a result of general tendency of the data to increase or decrease over a long period of time. This is also called long term trend or simply trend. The overall tendency may be increasing one as in population, price, number of automobiles on road and literacy. Decreasing nature may be in birth rate, infant mortality rate and poverty. Only very rarely constant nature is observed. Graphically linear trend is a straight line. Mathematically trend may be either i. ii. Linear or Non linear

SEASONAL VARIATIONS The changes that have taken place within a year as a result of change in climate, weather conditions, festivals etc. are called seasonal variations. Such change repeats itself year after year. Season is a period which is a part of one year. Certain variations are observed at some seasons and they are found to recur year after year. The factors which cause seasonal variations can be enumerated as below: i. ii. Climate and weather conditions Customs, traditions and habits

CYCLICAL VARIATIONS These are the changes that have taken place as a result of booms and depressions. Normally the period of cyclical variation is more than a year. Cyclical variation is similar to seasonal variation. If the changes take place periodically and if period is more than one year, the variations are said to be cyclical fluctuations. In business activities, there are some periods when the business activity is at its peak, while in some other periods it recedes and goes below the trend line. Cyclical variations do not follow any regular pattern. IRREGULAR VARIATIONS These are changes that have taken place because of forces that could not have been predicted like floods, earthquakes, famines etc.

One cannot say whether there would be rise or fall in a certain variable. Usually irregular variable are of smaller magnitudes. MODELS There are two types of mathematical models of time series. a) Additive model: When the changes in the data are the result of the combined impact of the four components, we can write the data as the sum of four components. i.e., Y = T + S + C + I Where, T= trend, S= seasonal variation, C= cyclical variation, I=irregular variation. b) Multiplicative model: In this mode original data, Y=TxSxCxI Where, T= trend, S= seasonal variation, C= cyclical variation, I=irregular variation. Many business and economic series agree with multiplicative model but additive model is found to suit only some series. MEASUREMENT OF TREND There are four methods to estimate the secular trend. They are i. Graphic method: - This is the simplest method for measuring trend of a time series. In this method the time series graph is drawn taking independent variable on the X axis and on the Y axis dependent variable is taken. The time values are plotted. This is called the time series graph or historiegram. Semi-averages method: - in this method the data is divided into two parts equally and the average of the values of each half together with the midpoint is plotted on the graph. The two points are so plotted and the straight line joining the two points is called trend line. Method of moving averages: - in this method the short time variations are eliminated by finding the moving averages. These moving averages indicate the trend. Method of least squares: - This is the most popular method of measuring the trend. In this method a mathematical relation is established between time and the variables which is depending on time. The relation may be linear, quadratic or exponential.

ii.

iii. iv.

MEASUREMENT OF SEASONAL VARIATIONS To obtain a statistical description of a pattern of seasonal variations it will be desirable to first free the data from the effects of trend, cycles and irregular variations. After eliminating these components the seasonal variations are measured in index form called seasonal index. Thus the measure of seasonal variations are called seasonal indices

There are various methods for measuring seasonal variations. Some of the popular methods are the following. i. ii. iii. iv. Method of Simple Averages Ratio to Moving Average Method Ratio to Trend Method Link Relative Method

MEASUREMENT OF CYCLICAL VARIATION In order to measure cyclical variations, it is necessary that the seasonal data are desesonalised and adjusted to trend. The resulting data comprises both cyclical and irregular variations. In order to isolate irregular variations from these data the irregular data must be smoothed out by using appropriate moving averages leaving only cyclic variations. MEASUREMENT OF IRREGULAR VARIATION An estimate of the irregular variations can be obtained from the following formula I= CI/C Where, I= irregular variation, CI = cyclical and irregular variation, C = cyclical variation In practice irregular variations are highly erratic and also both cyclic and irregular variations are so interwoven that it becomes extremely difficult to segregate from cyclic variation.

APPLICATIONS OF TIME SERIES ANALYSIS
Time series analysis has applications in a large number of areas. Some of the applications are given below i. Understand changing world temperature patterns ii. Economic Forecasting iii. Sales Forecasting iv. Budgetary Analysis v. Stock Market Analysis vi. Yield Projections vii. Process and Quality Control viii. Inventory Studies ix. Workload Projections x. Utility Studies xi. Census Analysis

Similar Documents

Free Essay

Time Series Analysis

...Time series analysis We are pleased to submit the following report on the “Time Series Analysis”. By completing the report, we have got acquainted importance and relevance of time series on business application. We also perceived idea on the whole process of Time Series Analysis. We acquired knowledge about the method of measuring trend, growth rate, acceleration rate etc. In spite of limitation of time & opportunity we have tried our level best to complete the report. We are pleased to provide you with this report with necessary analysis, references and we shall be available for any clarification, if required. Thank you for assigning us in this study. On behalf of the group Md. Arif Hasan ID: 12-150 Table of Contents Serial No Topic Page No 1 Letter of Transmittal 1 2 Rationale of the study 2 3 Objectives of the report 3 4 Methodology of the report 3 5 What is Time Series 4 6 Uses of Time Series in Business 5 7 Components of a Time Series 5 8 Classical Time Series Model 9 9 Methods of trend measurement 9 10 Least squares method 10 11 The Growth Rate 14 12 The Acceleration Rate 15 13 Rule of 72 16 14 Bibliography 17 Rationale of the study Having been assigned to prepare a report on Time Series Analysis we are submitting the term paper based on our findings and understandings. Time series analysis has vast application and is of huge importance in the field of Business and Economics as well as in decision making thereof. Calculating secular trend we......

Words: 2908 - Pages: 12

Free Essay

Time Series Analysis

...Time Series Analysis Yt=observed value of the time series in time period t TRt=the trend component or factorin time period t SNt=the seasonal componentor factorin time period t CLt=the cyclical componentor factorin time period t IRt=the irregular componentor factorin time period t 7.1) CL*IRCL=IR a) SN1=1.191 TR1=240.5 CL1=null IRt=null SN2=1.521 TR2=260.4 CL2=0.998 IR2=0.990 SN3=0.804 TR3=280.4 CL3=0.994 IR3=0.986 SN4=0.484 TR4=300.3 CL4=1.003 IR4=1.008 b) It presents a multiplicative decomposition model Yt=TRt*SNt*CLt*IRt SNt*IRt=YtTRt CLt snt*irt=YtCMAt =YtCMAt Equation of the estimated trend: TRt=Bo+B1t dt=B0+B1t+εt TRt=220.53+19.94(t) c) Yt=trt*snt Y17=220.53+19.9417*1.191=666.6 Y18=220.53+19.9418*1.521=881.6 Y19=220.53+19.9419*0.804=482.1 Y20=220.53+19.9420*0.484=299.9 d) Yt=trt*snt*cl We cannot see a definitive cycle and because the values of cl are close to 1. We do not take it into account. Y21=220.53+19.9421*0.191=761.6 e) Since there are just four years of data and most values are near 1 we cannot discern a well-defined cycle. f) Y21=220.53+19.9421*0.191=761.6 It agrees with the values computed in part c g) Excel Spreadsheet h) Prediction intervals for the next 4 quarters t=17,18,19,20 t=17:654.094,679.542 t=18:869.038,894.542 t=19:469.107,494.556 t=20:286.977,312.426 8.1) Smoothing equation l0=t=1nYtn Which is the average of the first series values lT=αyT+(1-α)lT-1 α:smoothing......

Words: 415 - Pages: 2

Free Essay

Time Series Analysis

...REPORT ON TIME SERIES ANALYSIS REPORT ON TIME SERIES ANALYSIS SUBMITTED TO M. KHAIRUL HOSSAIN PROFESSOR Department Of Finance University Of Dhaka SUBMITTED BY Group – 17 Section-A BBA 12th Batch Department Of Finance WE ARE... |Sl. No |Name |Roll No | |1. |Dulal Paul |12-143 | |2. |Rahat Hussain Md. Zaidy |12-149 | |3. |MD. Arif Hasan |12-150 | |4. |MD. Khurshid Alam |12-170 | |5. |MD. Saiful Islam |12-254 | Letter of Transmittal Date: 16th September, 2008 M. Khairul Hossain Professor Department Of Finance Faculty of Business Studies University of Dhaka Subject: Submission of report We are pleased to submit the following report on the “Time Series Analysis”. By completing the report, we have got acquainted importance and relevance of time series on business application. We also perceived idea on the whole process of Time Series Analysis. We acquired knowledge about the......

Words: 2921 - Pages: 12

Free Essay

Time Series Analysis Summary

...Time Series Analysis Summary Tokelo Khalema 2008060978 BSc. Actuarial Science University of the Free State Bloemfontein November 1, 2012 Time Series Analysis A time-series is a stochastic process {Xt : t = 1, . . . , T } with a continous state space and discrete time domain. It arises naturally as an ordered series of values observed over time. Examples include daily closing prices of a stock index recorded over several years, say, the flow rate of the River Nile, road casualties in Great Britain over the years 1969-84, etc. Stationary time-series are particularly easy to analyse. A series is stationary if its mean and variance are constant over time. Special aids are available to help determine whether or not a series is stationary. Particularly notable in this regard are the autocorrelation function (ACF) and the partial autocorrelation function (PACF). These are plots of the sample autocorrelation and partial autocorrelation coefficients at various time lags, respectively. If the ACF decays gradually to zero, then the series is non-stationary. If on the other hand the ACF and PACF decay rapidly to zero, then the series is stationary. A series being non-stationary can be brought about by, among others, a trend, irregular fluctuations, or seasonal variation. Non-constant variance, or as commonly called, heteroscedasticity can be eliminated by using a variance-stabilising transformation. A number of ways exist that eliminate a trend. Two of which are, to subtract a regression......

Words: 1929 - Pages: 8

Premium Essay

A Time Series Forecasting Analysis on the Monthly Stocks of Rice in the Philippines

...A Time Series Forecasting Analysis on the Monthly Stocks of Rice in the Philippines A Research Paper Presented To Dr. Cesar Rufino Of the Department of Economics School of Economics De La Salle University, Manila In Partial Fulfillment of the Course Requirements in Economic Forecasting (ECOFORE) Term 3 AY 2014-2015 Submitted by: Jayme, Kevin Matthew D. April 24 2015 0 I. Introduction The Philippines has been the accredited as an agricultural nation that provides different types of agricultural related goods, both for the domestic and international market. Rice has been the staple food in the Philippine to 80% of the population as it is customary diet that has been in beaded in the Philippine culture (Drilon Jr., 2012). Despite the strong history of agriculture and the skills and weather condition perfect for growth of rice, decrease of land and increase of total population around the Philippines decrease the opportunity for the population to have access to rice. In addition, neighboring countries, such as Thailand and Vietnam, had been on the rise of rice exportation. Not to mention the implementation of the ASEAN integration is happening in 2015. This means that the Philippines is lagging behind as it is the 8th largest exporters of rice in the world (Tiongco & Francisco, 2011). Institution, such as International Rice Research Institute (IRRI), has gone into research and development of rice growth in different conditions and......

Words: 2806 - Pages: 12

Premium Essay

Time Series Analysis

...Part I Task 1 Type of Property: Bungalow Location: Taman Tun Dr. Ismail, Kuala Lumpur |Number |Square Feet |Price (RM'000) | |1 |4500 |3280 | |2 |4800 |4180 | |3 |4500 |3300 | |4 |4500 |3300 | |5 |5000 |4100 | |6 |5000 |4700 | |7 |4000 |3300 | |8 |5000 |5000 | |9 |4352 |4000 | |10 |4000 |3300 | |11 |4000 |4000 | |12 |7000 |7800 | |13 |4352 |4000 | |14 |4300 |3280 | |15 |4000 |4300 | |16 |3800 |4500 | |17 |7000 |7800 | |18 |5000 |4700 | |19 |5650 |2600 | |20 |5000 |3880 | |21 |6000 |4180 | |22 ......

Words: 1820 - Pages: 8

Premium Essay

Financial Analysis Time Series

...the degree of financial development in a country, the wider will be the availability of financial services. A developed financial system offers higher returns with less risk. In this paper it is attempted to collect main components of financial development including Banks, Stock markets, insurance companies and bond markets for 41 economies during the period of 1988 to 2009. The method of principal component is utilized to extract a single financial development index out of them. Principal component analysis is a modern tool of data analysis. The main aim to apply principal component to achieve a meaningful index out of complex and multidimensional elements of financial development and to re-express the data with minimum noise and maximum extract, so that a single measure of financial development can be achieved. This index can be used to assess the financial strength of an economy and can be related to growth further. Key Words: Financial Development Index, Principal Component Analysis 1. Introduction Financial development can be defined as the policies, factors, and the...

Words: 10363 - Pages: 42

Premium Essay

Empirical Results

...CHAPTER 5. EMPIRICAL RESULTS, FINDINGS AND ANALYSIS 1. Over all graphical analysis For any index the best way to gauge its long term movement is to plot its movement over a period of time. So here to start with the analysis part , first the overall movement of the daily “close” data for S&P CNX NIFTY FIFTY is examined for the period starting from 2nd May 2002 till 3rd Feb 2012. There are in total 2347 observations and the econometric package EViews 7 has been used to track the movement. The plot is shown in Fig No 5.1. [pic] Fig No 5.1. Daily movement of Nifty Fifty “close” during 02/05/2002 – 03/02/2012 From the graph it is clear that Nifty has shown an upward trend over the period of time. While the upward trend is pretty evident from 2002 to 2007 however since 2007 Nifty movement has been somewhat unstable due to frequent market fluctuation and thus the market seems to be more volatile during this period. In terms of volatility another aspect is visible from the graph that is an upward trend is being followed by further upward trend while a downward trend is being followed by further downward trend and this feature is known as “volatility clustering” and this volatility clustering seems to be present in the index. More about the volatility and the movement of the index will be explored in the further subsections where the task of comparing Nifty movement at times is being taken. 2. Over all statistics The performance of Nifty over the years is......

Words: 4836 - Pages: 20

Premium Essay

Purefoods

...For example, height and weight are related; taller people tend to be heavier than shorter people. The relationship isn't perfect. People of the same height vary in weight, and you can easily think of two people you know where the shorter one is heavier than the taller one. Nonetheless, the average weight of people 5'5'' is less than the average weight of people 5'6'', and their average weight is less than that of people 5'7'', etc. Correlation can tell you just how much of the variation in peoples' weights is related to their heights. Although this correlation is fairly obvious your data may contain unsuspected correlations. You may also suspect there are correlations, but don't know which are the strongest. An intelligent correlation analysis can lead to a greater understanding of your data. Techniques in Determining Correlation There are several different correlation techniques. The Survey System's optional Statistics Moduleincludes the most common type, called the Pearson or product-moment correlation. The module also includes a variation on this type called partial correlation. The latter is useful when you want to look at the relationship between two variables while removing the effect of one or two other variables. Like all statistical techniques, correlation is only appropriate for certain kinds of data. Correlation works for quantifiable data in which numbers are meaningful, usually quantities of some sort. It cannot be used for purely categorical data,......

Words: 2622 - Pages: 11

Free Essay

Best Fitted Model to Forecast the Trade Balance of Malaysia

...The inclusion of five appropriate models in this study is purposely to examine the parameter values for comparison for error measures. Models involved are based on the Univariate Modelling Techniques; Naive with Trend Model, Single Exponential Smoothing, Double Exponential Smoothing, Holt’s Method Model and Adaptive Response Rate Exponential Smoothing (ARRES). The best parameter value obtained in this study marked as the main indicator in selecting the best fitted model; indicated by the smallest value of mean square error (MSE and MAPE). Based on the analysis, Adaptive Response Rate Exponential Smoothing (ARRES) model is the most suitable model to forecast the monthly Trade balance for Malaysia. Keywords: Fitted Model, Forecast, Parameter Value, Univariate Modelling Techniques, MSE, MAPE INTRODUCTION The balance of trade is the difference between the monetary value of exports and imports in an economy over a certain period of time. A positive balance of trade is known as a trade surplus and consists of exporting more than is imported while a negative balance of trade is known as a trade deficit or, informally, a trade gap. The balance of trade forms part of the current account for a particular country, which also includes other transactions such as income from the international investment position as well as international aid. A surplus in current account shows the country's net international asset position increases...

Words: 2922 - Pages: 12

Free Essay

Forecasting

...forecasting occurs when the future values of all explanatory variables are known with certainty. In conditional forecasting, errors may be huge because we first must forecast values of the explanatory variables. Only unconditional forecasts are free of these errors. Contingency forecasting involves generating several forecasts, one for each alternative set of circumstances, or "scenario," that is likely to arise. The estimation period is the time series data used to fit a forecasting model. Ex post forecasting involves "forecasting" the most recent observations after withholding them from the estimation period. By contrast, ex ante forecasting uses an estimation period that includes the most recent observations. Ex post forecasting is a valuable method for evaluating performance of time series models. Before making a judgment, however, forecast several observations, examine model performance under different number of periods forecast, consider only models defensible on prior grounds, and include conditional forecasting errors in your analysis....

Words: 477 - Pages: 2

Premium Essay

Operations Management Krajewski Chpt 13

...known as a time series. Answer: True Reference: Demand Patterns Difficulty: Easy Keywords: time series, repeated observations 2. One of the basic time series patterns is trend. Answer: True Reference: Demand Patterns Difficulty: Easy Keywords: time series, pattern, trend 3. One of the basic time series patterns is random. Answer: True Reference: Demand Patterns Difficulty: Easy Keywords: time series, pattern, random 4. Random variation is an aspect of demand that increases the accuracy of the forecast. Answer: False Reference: Demand Patterns Difficulty: Easy Keywords: random variation, forecast accuracy 5. Aggregation is the act of clustering several similar products or services. Answer: True Reference: Key Decisions on Making Forecasts Difficulty: Moderate Keywords: aggregation, clustering 6. Aggregating products or services together generally decreases the forecast accuracy. Answer: False Reference: Key Decisions on Making Forecasts Difficulty: Moderate Keywords: aggregation, forecast accuracy 54 Copyright ©2010 Pearson Education, Inc. Publishing as Prentice Hall Chapter 13 • Forecasting 7. Judgment methods of forecasting are quantitative methods that use historical data on independent variables to predict demand. Answer: False Reference: Key Decisions on Making Forecasts Difficulty: Moderate Keywords: judgment method, forecast, historical data, qualitative methods 8. Time-series analysis is a......

Words: 13527 - Pages: 55

Premium Essay

Forecast Trend

...the period 1965 to 2004 is selected and the hold-out 2005 to 2009 is used to examine the out-of-sample forecasting performance. To begin with, the GDP –China graph is plotted by using the STATA command in order to check overall the trend. Next, it is necessary to tell the STATA that this dataset is the time series format by using “tsset time” command. Then, the autocorrelations and partial autocorrelation are used to examine that whether the series is non-stationary or not. As can be seen the autocorrelation and partial autocorrelation graph below, they can be suggested that the series is non-stationary because the AC graph The series is non-stationary as the autocorrelations decrease slowly as the number of time lags increases and the partial autocorrelations show a large spike close to one at lag 1. Autocorrelation (AC) Partial autocorrelations (PAC) To estimate the fitted model, there are four possible trends that are chosen to compare as follows: Linear trend model In order to forecast the trend, we start to fit a linear trend model to the data by regressing the GDP on a constant and a linear time trend. The p-value of the t- statistic on the time trend is zero and the regression’s R2 is high so it can be implied that the trend appears highly significant. Moreover, as can be seen in the residual graph, it can be concluded that the linear trend is inadequate due to the fact that the actual trend is nonlinear. Residual Additionally, the......

Words: 1122 - Pages: 5

Premium Essay

Fdi in Bangladesh

...Foreign direct investment And Economic Growth in Bangladesh Internship program at Brac Bank Ltd. Internship Report On “Foreign direct investment And Economic Growth in Bangladesh and Internship program at Brac Bank Ltd.” The Internship report is submitted to the Department of Finance, University of Dhaka for the partial fulfillment of the requirement of BBA program. Submitted to: Department of Finance University of Dhaka Supervised by: Mohammad Jahangir Alam Chowdhury Professor Department of Finance University of Dhaka Submitted by: Zarin Tasnim ID: 17-009 Section: A Department of Finance University of Dhaka Signature of the Supervisor Date of Submission: 7th May, 2015 Letter of Transmittal 7th May, 2015 Mohammad Jahangir Alam Chowdhury Professor Department of Finance University of Dhaka Subject: Submission of Internship Report on Foreign direct investment and Economic Growth in Bangladesh. Dear Sir, It is an absolute pleasure for me to submit the Internship Report titled “Foreign direct investment and Economic Growth in Bangladesh” as a significant part of the BBA program. While making this report, I have experienced a fair knowledge about Foreign direct investment and economy of Bangladesh and its impact on the growth of Bangladesh. I have tried my best to follow your guidelines in every aspect of preparing this report. I have collected what I......

Words: 13995 - Pages: 56

Premium Essay

Math Student

... What is Forecasting?   Forecasting Time Horizons The Influence of Product Life Cycle  Types of Forecasts  The Strategic Importance of Forecasting    Human Resources Capacity Supply-Chain Management  Seven Steps in the Forecasting System 4-2 Outline - Continued  Forecasting Approaches   Overview of Qualitative Methods Overview of Quantitative Methods  Time-Series Forecasting         Decomposition of Time Series Naïve Approach Moving Averages Exponential Smoothing Exponential Smoothing with Trend Adjustment Trend Projections Seasonal Variations in Data Cyclic Variations in Data 4-3 Outline - Continued Associative Forecasting Methods: Regression and Correlation Analysis Using Regression Analysis to Forecast  Standard Error of the Estimate  Correlation Coefficients for Regression Lines  Multiple-Regression Analysis  Monitoring and Controlling Forecasts Adaptive Smoothing  Focus Forecasting  Forecasting in the Service Sector 4-4 Learning Objectives When you complete this chapter, you should be able to : Identify or Define: Forecasting  Types of forecasts  Time horizons  Approaches to forecasts  4-5 Learning Objectives - continued When you complete this chapter, you should be able to : Describe or Explain: Moving averages  Exponential smoothing  Trend projections  Regression and correlation analysis  Measures of forecast......

Words: 2444 - Pages: 10