3.1A small regional trucking company has experienced steady growth. Use time series regression to forecast capital needs for the next 2 years. The company's recent capital needs have been:
══════════════════════════════════════════════
Capital Needs Capital Needs
(Thousands Of (Thousands Of
Year Dollars)Year Dollars)
------------------------------------------- --------------------------------------------
1100 3130
2110 4140
5160
══════════════════════════════════════════════ perform a regression analysis and forecast sales for the next two years:

Exponential Smoothing

3.33The Sporting Charge Company buys large quantities of copper that is used in its manufactured products. Bill Bray is developing a forecasting system for copper prices. He has accumulated this historical data:

a.Use exponential smoothing to forecast monthly copper prices. Compute what the forecasts would have been for all the months of historical data for = 0.1, = 0.3, and = 0.5 if the forecast for all ’s in the first month was $0.99.

b.Which alpha () value results in the least mean absolute deviation over the 16-month period?

c.Use the alpha () from Part b to compute the forecasted copper price for Month 17.

Integrated Products Corporation (IPC) needs to estimate its sales for next year. The most recent six years of revenue data for the company’s line of XT computers are found in the table below:

...Regression with TimeSeries Data Week 10
Main features of Timeseries Data
Observations have temporal ordering
Variables may have serial correlation, trends and seasonality
Timeseries data are not a random sample because the observations in timeseries are collected from the same objects at different points in time
For timeseries data, because MLR2 does not hold, the inference tools are valid under a set of strong assumptions (TS1-6) for finite samples
While TS3-6 are often too restrictive, they can be relaxed for large samples. In essence, TS1, TS2, (z10), (h10) and (u10) are sufficient for large sample inference
Serial correlation of a timeseries variable is the correlation between the variable at one point in time with the same variable at another point in time
(z10), (h10), (u10)
z10 = E(ut | xt) = 0
When (z10) holds then the regressors are contemporaneously exogenous and OLS is consistent but is not sufficient for OLS to be unbiased
When TS3 holds, which implies (z10), then the regressors are strictly exogenous and OLS is unbiased
h10 = Var(ut | xt) = 2 and is known as contemporaneous homoskedasticity and is a weaker assumption than TS4
u10 = E(utus | xt,xs) = 0 and is a weaker assumption than TS5
FDL model and LRP
A FDL model...

...SECTION A (You should attempt all 10 questions)
A1. Regression analysis is ____________________________________.
A) describes the strength of this linear relationship.
B) describes the mathematical relationship between two variables.
C) describes the pattern of the data.
D) describes the characteristic of independent variable.
A2. __________________ is used to illustrate any relationship between two variables.
A) Histogram
B) Pie chart
C) Scatter diagram
D) Frequency polygon
Questions A3 to A5 relate to the following information.
Suppose a firm fed the values of turnover, y, and advertising expenditure, x, (both in $000) for the past eight years, into a computer and obtained the regression relationship y = 26.7 + 8.5x.
A3. What is the dependent variable?
A) Number of computers
B) Size of the firm
C) Turnover
D) Advertising expenditure
A4. What is the independent variable?
A) Number of computers
B) Size of the firm
C) Turnover
D) Advertising expenditure
A5. If the advertising expenditure is $5000 in a particular year, estimate the turnover for that year.
A) $69,200
B) $42,526.70
C) $26.7
D) $69.20
A6. Explain what the following sample correlation coefficients tell you about the relationship between the x and y values in the sample:
r = - 0.8
A) No correlation....

...This paper is a report on the time-series analysis of continuously compounded returns for Ford and GM for the periods January 2002 till April 2007 using monthly stock prices. This analysis is aimed at estimating the ARIMA model that provides the best forecast for the series. This paper will be divided into 2 sections; the first section showing the Ford analysis and the second the GM analysis.
Section 1: Ford
Figure 1: Timeseries plot for raw Ford data.
Figure 1 shows a timeseries plot of the raw Ford stock prices against time. From this plot, a gradual but continuous upward trend can be observed. This trend was disrupted in 2005 when the stock prices experienced a huge rise moving from below 5 to above 25. This rise in stock price by Ford was not sustained as can be seen from the plot; the prices which reached a peak of above 25 fell to a about 10 by the end of 2005 and fell further in 2006 to a level below 5 fluctuations in the stock price existed and in 2007 the prices began to level out.
Raw data is likely to be affected by non-stationarity and this can result in bias in the analysis. For the purpose of this analysis, it is required that the returns be continuously compounded. To achieve this I have taken the log and first difference of the raw data: this also achieves stationarity in the timeseries data....

....2.3 Timeseries models
Timeseries is an ordered sequence of values of a variable at equally spaced time intervals. Timeseries occur frequently when looking at industrial data. The essential difference between modeling data via timeseries methods and the other methods is that Timeseries analysis accounts for the fact that data points taken over time may have an internal structure such as autocorrelation, trend or seasonal variation that should be accounted for. A Time-series model explains a variable with regard to its own past and a random disturbance term. Special attention is paid to exploring the historic trends and patterns (such as seasonality) of the timeseries involved, and to predict the future of this series based on the trends and patterns identified in the model. Since timeseries models only require historical observations of a variable, it is less costly in data collection and model estimation.
. Timeseries models can broadly be categorized into linear and nonlinear Models. Linea models depend linearly on previous data points. They include the autoregressive (AR) models, the integrated (I) models, and the moving average (MA) models. The general autoregressive...

...TimeSeries Models for Forecasting New One-Family Houses Sold in the United States
Introduction
The economic recession felt in the United States since the collapse of the housing market in 2007 can be seen by various trends in the housing market. This collapse claimed some of the largest financial institutions in the U.S. such as Bear Sterns and Lehman Brothers, as they held over-leveraged positions in the mortgage backed securities market. Credit became widely available to unqualified borrowers during the nineties and the early part of the next decade which caused bankers to act predatorily in their lending practices, as they could easily sell and package subprime mortgage loans on leverage. This act caused a bubble that would later burst when unqualified homebuyers began defaulting on their loans causing a tremendous downfall in the U.S housing market. Understanding which direction key market factors, such as the housing market, are going can help re-establish stability in the market, which is at an all-time premium. This paper is designed to help better predict the direction of the housing market in the future via the use of timeseries models, in an effort to re-establish a sense of stability in the housing market.
The Data Pattern of New One-Family Houses Sold in the U.S.
The following chart (Figure 1) represents the timeseries data for non-seasonally adjusted home...

...MGMT E 5070 DATA MINING AND FORECAST MANAGEMENT Professor Vaccaro 1st EXAMINATION , ( Forecast Error, TimeSeries Models, Tracking Signals ) NAME____________________ Solution True or False 1. T F According to the textbook, a short-term forecast typically covers a 1-year time horizon. 2. T F Regression is always a superior forecasting method to exponential smoothing. 3. T F The 3 categories of forecasting models are timeseries, quantitative, and qualitative. 4. T F Time-series models attempt to predict the future by using historical data. 5. T F A moving average forecasting method is a causal forecasting method. 6. T F An exponential forecasting method is a time-series forecasting method. 7. T F The Delphi method solicits input from customers or potential customers regarding their future purchasing plans. 8. T F The nave forecast for May, for example, is the actual value observed in April. 9. T F Mean absolute deviation ( MAD ) is simply the sum of the forecast errors. 10. T F Four components of timeseries are trend, moving average, exponential smoothing, and seasonality. 11. T F In a weighted moving average, the weights assigned...

...A timeseries analysis for Chinese Electricity Demand
1. Introduction
Electricity is the basic demand for peoples’ daily life, and relate to the Industrial production. It is also be a very important indexer to indicate the economic growth because the electricity demand and the economic growth always highly related. Thus the prediction of the electricity demand is very important. The government of a country must be able to forecasting the electricity demand in order to formulate its policies. This paper will conduct an analysis for the Chinese Electricity demand, and provide some useful model to predict the electricity demand in the future.
2. Timeseries data for Electricity demand of China
Monthly electricity generation of China from 1999 to 2004 is shown in table 1. Plot the data on Figure 1, it can be shown that the demand of electricity was growing during these six years. From the chart, the growth trend can be easily indentified. The pattern of the trend will be discussed in following section. The monthly electricity data present some seasonal changed pattern, the July and August seem like the peak of each year, more detail should be discussed in later section.
Table 1: Chinese Monthly Electricity Generation
Source: Chinese yearly statistical Data, www.stats.gov.cn
Figure 1: Electricity Generation plot versus time
3. Modelling trend by using Polynomial Functions
From the plot...

...HTime series using Holt-Winters Forecasting Procedure
Summary
The Holt-Winters forecasting procedure is a simple widely used projection method which can cope with trend and seasonal variation.
We can apply this method to lots of fields such as banking data analysis, investment forecasting, inventory controlling and so on.
This paper shows us a practical banking credit card example using Holt-Winter method in Java programming for data forecasting.
The reason we use Holt-Winter is that this method is simple while generally works well in practice, and is particularly suitable for producing short-term forecasts for sales or demand time-series data.
Theorem
Xt(1)= Lt+ Tt+ It-p+1
Xt(h)= Lt+ hTt+ It-p+h
Lt= Lt-1+ Tt-1+ αet
Tt= Tt-1+ αγet
It= It-p+ δ(1-α)et
Xth=Lt+ hTt* It-p+h for h=1,2,… ,p
Lt= αXtIt-p+(1-α)(Lt-1+ Tt-1)
Tt= γ(Lt-Lt-1)+ 1-γTt-1
It= δXtLt+(1-δ)It-p
et= Xt-Xt-1(1)
There are two types of seasonal model: an additive version which assumes that the seasonal effects are of constant size and a multiplicative version which assumes that the seasonal effects are proportional in size to the local deseasonalized mean level. Both seasonal models assume that the local deseasonalized mean level may be modified by an additive trend term and also that there is an additive error term of constant variance.
Suppose we have an observed timeseries, denoted by X1, X2, …, Xn , and wish...

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