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# Time Series Analysis

A time series is a sequence of data points measured at successive points in time spaced at uniform time intervals.  Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance and many more. Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistic and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values. Regression analysis is often employed in a way to test theories that the current values of one or more independent time series affect the current value of another time series, this analysis of time series is not called “time series analysis”. It focuses on comparing values of time series at different points in time.

Time series data have a natural temporal ordering. It makes time series analysis distinct from other data analysis problems in which there is no natural ordering of the observations. Time series analysis is also distinct from spatial data analysis where the observations typically relate to geographical locations. Time series models will often make use of the natural one-way ordering of time so that values for a given period will be expressed as deriving in some way from past values, rather than from future values. Time series analysis can be applied to real-valued, continuous data, discrete numeric data or discrete symbolic data.

Models for time series data can have many forms and represent different processes. When modeling variations in the level of a process, the three broad classes of practical importance are the autoregressive models, the integrated models and the moving average models.

### Science and Technology Mutual Fund

Emily Andrews has invested in a science and technology mutual fund. Now she is considering liquidating and investing in another fund.She would like to forecast the price of the science and technology fund for the next month before making a decision.She has collected the following data onthe average price of the fund during the p

### Weighted Average Forecasting

Perform a weighted average forecasting with weights 0.5, 0.3 and 0.2, starting with the most recent month, for the following data. Month Demand January 21 February 23 March 34 April 32 May 33 June 35 July 30 August 26 September 24 October 25 November 26 December 28

### Steps on Calculating Uniform Annual Cost

An alternative has a discounted project cost of \$12,345,000 with a discounted salvage value of \$1,750,000. The estimate was in constant dollars and the discounting used end-of-year factors. While the period of analysis is 5 years, the alternative only provides benefits for the last 4 years. Calculate the uniform annual cost.

### Constructing a p chart for given data using excel

Researchers at Miami University in Oxford, Ohio, investigated the use of charts to monitor the market share of a product and to document the effectiveness of marketing promotions, Market share is defined as the company's proportion of the total number of products sold in a category. If a p chart based on a company's market share

### Marginal Analysis - Profit Maximization

Ayang imchem is the manager of casto cheese, which produces cheese spreads and other cheese related products. E-Z spread cheese is a product that has always been popular. The probability of sales, cases, is as follows: Demand (cases) Probability 10 0.2 11 0.3 12 0.2 13 0.2 14 0.1 A case of E-Z spread cheese sells for \$

### Some discussion on crude rate ratio and corresponding rate ratio

The crude rate ratio between white and blacks is 1.34. The corresponding rate ratio based on the age-adjusted rates is 1.0 What does this tell you about the age distribution among the geographic population

### Simulation study for arrival time, service time and waiting time

During the dinner hour, the distribution of the inter-arrival time of customers at a restaurant is estimated to be as shown below. The mode of payment and the service times of the cash and credit card customers are shown in the following tables. Complete the tables and simulate the system for 20 customer arrivals and determine

### Various questions on quantitative analysis for management

I have most of the answers, I just need to make sure I know how to read the charts/data, with the proper steps. I want to be able to study the correct info. The question is on the topic of quantitative analysis for management and includes questions about finding the critical path and calculating slack time.

### Smoothing Techniques

I have been using basic smoothing techniques such as moving average, median smoothing and exponential smoothing to generate forcasts for the time series in the attached excel file. I would like to know if more advanced smoothing techniques would give better results. The columns in the file are a time series of performance fig

### Autocorrelation Function and Partial Autocorrelation Function

The instructor has "covered" Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF), but I have not yet grasped a full understanding. Could you give me a cursory explanation now? I do know how to call up the ACF and PACF graphs but her explanation of how to use them and what they mean was not very clear.

### Time-series plots and stock prices

The S&P 500 Index tracks the overall movement of the stock market by considering the stock prices of 500 large corporations. The attached file (Stock Prices) contains weekly data for this index as well as the daily closing stock prices for three companies from January 2, 2008, to January 12, 2009. The following variables are inc

### Time-series plot

The attached excel sheet contains the weekly average price of gasoline in the United States from January 1, 2007, to January 12, 2009. Prices are in dollars per gallon. A) Construct a time-series plot B) What pattern, if any, is present in the data?

### Statistics Problem: Merger Trends

The accompanying data indicate the number of mergers that took place in an industry over a 19-year period. Year Mergers Year Mergers Year Mergers 1 23 8 64 14 150 2 23 9 47 15 165 3 31 10 96 16 192 4 23 11 125 17 210 5 32 12

### Time Series Graphing

The marketing manager of a company that manufactures and distributes heavy-duty equipment used in the road construction industry recorded the number of farming units sold quarterly for the period 2007 to 2012. The data is displayed in the table below. 2007 2008 2009 2010 Summer 70 74 79 78 Autumn 6

### Time Series: Equation Derivation

Can you derive the equation for: Corr(Xn, Xn-1) (i.e. the normalized correlation) Given the model Xn= A*Xn-1 + (epsilon)n Where: epsilon=N(0,var), A is a constant I tried to use a double sum but I got very confused.

### Moving Averages for the Time Series

The following data represent revenues in thousands of dollars for a manufacturer of small electric appliances. a. Calculate the moving averages for this time series. Moving Year Quarter Revenues Q Average 1996 1 514

### Time Series Analysis Verify

Question 1 Suppose that {Y_t} is stationary with autocovariance function ?_k. a) Show that W_t=?Y_t=Y_t-Y_(t-1) is stationary by finding the mean and autocovariance function for {W_t} . b) Show that U_t=?^2 Y_t=?[Y_t-Y_(t-1) ]= Y_t-2Y_(t-1)+Y_(t-2) is stationary. (you need not find the mean and autocovariance function for

### Time Series Analysis and Random Processes

Question 1: Simulate a completely random process of length 48 with independent, normal values. Plot the time series plot. Does it look "random"? Repeat this exercise several times with a new simulation each time. Question 2: Simulate a completely random process of length 48 with independent, t-distributed values each with 5

### Time series and Statistical Control Process: Variables, parameters, linear equation

If the sales, employment, production, and other business series increase or decrease over a period of time and approximate a straight line, the equation for this growth is given by Y= bX + a, the linear trend equation. Part 1: State the dependent and independent variables. Also, state wha

### Statistics - Time Series

(a) Choose one time-series describing Airlines and make a line chart. (b) Describe the trend (if any) and discuss possible causes. (c) Fit both a linear and an exponential trend to the data. (d) Which model is preferred? Why? (e) Make a forecast for 2003, using a trend model of your choice (or a judgment forecast).

### Ratio to Moving Average Method

Ratio to moving average method An analyst wants to use the ratio-to-moving average method to forecast a company's sales for the next few quarters. Beginning in Quarter 4 of 2005, the analyst collects the following sales data (in millions of dollars). Estimate the seasonal index associated with Quarter 3. Round your answer to

### Forecasting the number of repair orders

An appliance repair shop owner has fitted the quadratic trend equation y = 90 + 0.9x + 3x2 to a time series of annual repair orders, with y = the number of repair orders and x = 1 for 2000. Forecast the number of repair orders for 2008; for 2010.

### Time Series analysis

The following is a time series data set. Run a time-series analysis for projections of April 2009 in the Healthcare industry of Nashville. (Run in SPSS and just copy and paste results in microsoft word. Explain your results) 2006-Dec 55010 2006-Nov 55200 2006-Oct 54100 2006-Sep 54050

### linear trend of time series

For the data of this exercise use the weighting constant  = 0.5 and exponential smoothing to determine the forecast for 2005. U.S. cellular phone subscribership has been reported as shown below for the 1993-2004 period Year Subscribers (millions) Year Subscribers (millions) 1993 16.0 1999 86.0 1994 24.1 2000 109.5 1995 3

### Short-Term Forecasting

Data covering the most recent 30 days are given in the following table for the price per gallon of regular gasoline at a location station Day Price Day Price 1 2.53 16 2.46 2 2.35 17 2.6 3 1.91 18 2.1 4 2.2 19 2.01 5 1.77 20 2.14 6 3.26 21 2.03 7 1.63 22 2.68 8 2.73 23 2.59 9 2.41 24 2.99 10 2.72 25 2.94 11 2.87

### Determine a typical seasonal index for each of the four quarters.

Victor Anderson, the owner of Anderson Belts, Inc., is studying absenteeism among his employees. His workforce is small, consisting of only five employees. For the last three years he recorded the following number of employee absences, in days, for each quarter. Quarter Year I II III IV 2001 4 10 7 3 2002 5 12 9 4 2003 6

### How to do overall adequate at 0.05 level, moving average and 2 others questions

1. The overall model statistically adequate at a 0.05 level of significance for predicting sale price(y)? a. no, since some other t-tests for the individual variables are not significant. b. no since the standard deviation of the model is fairly large. c. yes, since none of the B -estimates are equal to 0. d. yes, since

### Statistics Study Guide

Questions 12 - 19 refer to the attachment : Product sales since 1984 are: Year 1984 1985 1986 1987 1988 1989 1990 1991 1992 Sales 266 264 145 205 139 98 94 94 128 The least squares trend equation using the coded method is given: Y1 = 159.22 - 21.18X, where X is set equal to 0 for 1

### Statistics - Time series equation - non-linear trend

Mabel's is open from 8AM til 2 PM to serve breakfast and lunch Her accountant has said that he can take the number of customers over the last three years and predict the volume for the next year Year Time Period Customers 2003 8-10 1200 10-12 1412 12-2 1810 2004 8-10 1320 10-12 1520 12-2 2102 20

### Estimation of trend in Time series by method of least squares

Estimation of trend in Time series by method of least squares. See attached file for full problem description.