...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 can...
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...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 constant ...
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...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...
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...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 line...
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...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 situation...
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...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 |5200...
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...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...
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...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 tabulated...
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...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, such...
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... 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 accuracy 4-6 ...
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...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....
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...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...
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...not work, use File.xls Choice of sample period: Sample / @all @first @last 1990 2010 1981Q3 2005Q1 1960M1 2000M11 in command line e.g.: smpl @first 1990 Univariate statistics: Click series / View / Spreadsheet Graph Descriptive Statistics&Tests Correlogram data as numbers Graphics z.B. histogram, mean, etc. autocorrelationen Generation/Transformation of series: Generate / x = 0 generates a series with zeros Generate / pi = (pc – pc(-1))/pc(-1)*100 Generates the inflation rate in % based on prices pc Generate / x = log(y) taking logs Generate / dlx = dlog(x) dlx = log(x) – log(x(-1)) Growth rate in continuous time Generate / y = exp(x) exp(x) as command: series x=0 Trend variable (linear): Generate / t = @trend Standard normal distributed realizations: Generate / x = nrnd Lags, lagged variables, taking differences: Generate / x1 = x(-1) x1(t) = x(t-1), Lag 1 of x Generate / dx = d(x) dx(t) = x(t) – x(t-1) = (1-B)x(t) first difference Generate / d2x = d(x,2) d2x(t) = dx(t) – dx(t-1) = (1-B)^(2)x(t) taking first differences twice Generate / d12x = d(x,0,12) d12x(t) = x(t) - x(t-12) = [1-B^(12)]x(t) seasonal difference for monthly data Generate d12_1x = d(x,1,12) d12_1x(t) = (1-B)[1-B^(12)]x(t) Geneartion of dummy variables: seasonal dummies: s=1,2,3,... Generate / ds = @seas(s) as command: series ds = @seas(s) Generate / d1 = 0 and manually in View/Spreadsheet use Edit+/p-value for x of a test statistic as command: (N-, t-, scalar p scalar p scalar p scalar p scalar p ...
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...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 linear...
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...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 statistical...
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