StudentShare
Contact Us
Sign In / Sign Up for FREE
Search
Go to advanced search...

Time Series Analysis, Forecasting and Control - Essay Example

Cite this document
Summary
This essay "Time Series Analysis, Forecasting and Control" discusses the time series concepts. In the first part, we begin by looking at the stationarity of the data set using the Augmented Dickey-Fuller (ADF) test. The next section presents an estimation of the ACF and the PACF…
Download full paper File format: .doc, available for editing
GRAB THE BEST PAPER96.3% of users find it useful
Time Series Analysis, Forecasting and Control
Read Text Preview

Extract of sample "Time Series Analysis, Forecasting and Control"

Download file to see previous pages

Augmented Dickey-Fuller tests

The following table gives the results of the ADF test conducted in gretl;

The following hypothesis was to be tested using the ADF test;

  • H0: δ = 0 (there is a unit root)
  • HA: δ ≠ 0 (there is not a unit root)

The computed value of the ADF test is –1.782, its asymptotic p-value is greater than 5% (0.7137). Hence the null of nonstationarity cannot be rejected (there is a unit root).

Autocorrelation Function (ACF)

Autocorrelation function (ACF) is the cross-correlation of a signal with itself. It refers to the similarity between observations as a function of the time lag between them. ACF is a statistical tool for finding repeating patterns, for example, the presence of a periodic signal obscured by noise, or maybe identifying the missing fundamental frequency (Box and Jenkins, 1994) in a signal implied by its harmonic frequencies. 

Partial Autocorrelation Function (PACF)

Just like ACF, PACF plots (Box and Jenkins, 2008) are also commonly used tools for identifying the order of an autoregressive model. The partial autocorrelation of an AR (p) process is zero at lag p + 1 and greater. If the sample autocorrelation plot indicates that an AR model may be appropriate, then the sample partial autocorrelation plot is examined to help identify the order. One looks for the point on the plot where the partial autocorrelations for all higher lags are essentially zero. Placing on the plot an indication of the sampling uncertainty of the sample PACF is helpful for this purpose: this is usually constructed on the basis that the true value of the PACF, at any given positive lag, is zero.

The figure below gives the ACF and PCF plots;

If the PACF displays a sharp cut-off while the ACF decays more slowly (i.e., has significant spikes at higher lags), we say that the stationaries series displays an "AR signature," meaning that the autocorrelation pattern can be explained more easily by adding AR terms rather than by adding MA terms. The plots clearly display a sharp cut-off for the PACF and a significantly reduced value of spikes for the ACF implying that we instead use an AR model.

Part 3

From the ACF and PACF plots above, it is clear that our best choice is an AR model and as such we present the ARMAX model. The model was estimated in Gretl using the Conditional Maximum Likelihood

Model 2: ARMAX, using observations 1981:10-2014:12 (T = 399)

Dependent variable: timeseriesdata

 

Coefficient

Std. Error

z

p-value

 

const

0.846273

0.322733

2.6222

0.00874

***

phi_1

0.992877

0.00598555

165.8792

<0.00001

***

theta_1

0.552444

0.0438309

12.6040

<0.00001

***

Timeseriesperiod

0.00434338

0.0035137

1.2361

0.21641

 

 

Mean dependent var

 162.7706

 

S.D. dependent var

 68.02335

Mean of innovations

−0.001507

 

S.D. of innovations

 1.036725

Log-likelihood

−580.5472

 

Akaike criterion

 1171.094

Schwarz criterion

 1191.039

 

Hannan-Quinn

 1178.994

 

 

 

Real

Imaginary

Modulus

Frequency

AR

 

 

 

 

 

 

Root 1

1.0072

0.0000

1.0072

0.0000

MA

 

 

 

 

 

 

Root 1

-1.8101

0.0000

1.8101

0.5000

 

LM test for autocorrelation up to order 12 -

 Null hypothesis: no autocorrelation

 Test statistic: Chi-square(10) = 83.8796

 

Estimation

In this section, we present the values of the forecasts for the last 10% data values;

269.93

276.93

283.96

291.03

270.62

277.63

284.67

291.74

271.32

278.33

285.37

292.44

272.02

279.03

286.08

293.15

272.72

279.74

286.78

293.86

273.42

280.44

287.49

294.57

274.12

281.14

288.20

295.28

274.82

281.85

288.90

295.99

275.52

282.55

289.61

296.70

276.22

283.26

290.32

297.41

 

 

...Download file to see next pages Read More
Cite this document
  • APA
  • MLA
  • CHICAGO
(“Time Series Assignment Essay Example | Topics and Well Written Essays - 1500 words”, n.d.)
Time Series Assignment Essay Example | Topics and Well Written Essays - 1500 words. Retrieved from https://studentshare.org/finance-accounting/1673316-time-series-assignment
(Time Series Assignment Essay Example | Topics and Well Written Essays - 1500 Words)
Time Series Assignment Essay Example | Topics and Well Written Essays - 1500 Words. https://studentshare.org/finance-accounting/1673316-time-series-assignment.
“Time Series Assignment Essay Example | Topics and Well Written Essays - 1500 Words”, n.d. https://studentshare.org/finance-accounting/1673316-time-series-assignment.
  • Cited: 1 times

CHECK THESE SAMPLES OF Time Series Analysis, Forecasting and Control

Various Types of Time Series Analysis

time series analysis There are two types of analysis schemes, namely the qualitative analysis technique and the quantitative mode of analysis technique.... 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.... 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....
8 Pages (2000 words) Essay

Business Forecasting

These techniques are utilized in the several fields of management from marketing and sales to the inventory control to avoid unwanted hassles and manage.... This enables control and management of resources better than doing in any other way.... The analysis is done to analyze and identify the appropriate model of forecasting for the softwood unfilled orders forecasting.... The number of data and the variables present are the basis to analyze it for the further forecasting process....
6 Pages (1500 words) Essay

Business forecasting

In the paper 'Business forecasting' the author analyzes business forecasting, which refers to the process used in estimating and predicting future patterns in business using business data, forecasting is essential in business, it helps in informing decisions concerning activities.... The author states that business forecasting is done on short-term, long-term, and medium depending on the particular application.... Budgeting involves use of forecasting techniques, it is an organization-wide process and is central in strategic planning....
5 Pages (1250 words) Essay

Time Series Data Mining and Forecasting Using SQL Server 2008

The data can then be explored followed by analysis through the use of multiple important tools or methodologies that are developed using modernized time series analysis.... This thesis "time series Data Mining and Forecasting Using SQL Server 2008" carries out data mining using the records on the production of major crops in Ghana for the past forty years as the data source.... In view of the increasing utilization of modern information technology, we use data on the production of some major crops in Ghana over the past forty years as a case to help in illustrating the manner in which data mining is applicable in such a time series helping the state to witness the benefits of such efforts....
64 Pages (16000 words) Thesis

Econometric analysis project

time series analysis is a form of statistical data analysis on a series of sequential data points that are usually measured at uniform time intervals over a period of time.... time series analysis is the estimation of difference equations containing stochastic (error) terms (Enders 2010).... Therefore, many approaches and models have to be developed in order to utilize the time series analysis and provide an accurate prediction of what is to come in the future....
5 Pages (1250 words) Statistics Project

Financial Econometrics

ime Series Analysis: forecasting and control.... time series analysis.... TIMESLAB: A time series analysis Laboratory.... PACF is Econometrics Log of Real Personal Disposable Income (Lrpdi) The graph above is a time series plot for the log of real personal disposable income.... Introduction to time series Using Stata.... Distribution of the estimators for autoregressive time series with a unit root....
2 Pages (500 words) Assignment

Regression Modelling and Analysis

time series analysis and forecasting are also discussed in detail and further research recommendations are provided in the conclusion part of the paper.... The research paper, Regression Modelling and analysis, provides a complete explanation of the various regression methods, detailed explanation of the regression line using the least square methods and also the interpretation of the regression line.... The research discussion provides a complete, clear and concise explanation of all the aspects of regression modeling and regression analysis....
7 Pages (1750 words) Term Paper

Forecasting for Healthcare

The seasonal pattern is a time series although the example illustrated herein shall not dwell on the error calculation but shall indicate the basics of what is supposed to be done in way of fulfilling this study.... Apart from medical supply chain management, forecasting has demonstrated usefulness in modeling for operations such as inventory control, personal investments and budgeting in various government agencies.... The paper "forecasting for Healthcare" describes that the trends in forecasting for healthcare are dynamic depending on the determining factors....
10 Pages (2500 words) Research Proposal
sponsored ads
We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.
Contact Us