ARIMA/GARCH (1,1) MODELLING AND FORECASTING FOR A …

ELK ASIA PACIFIC JOURNAL OF MARKETING AND RETAIL MANAGEMENT ISSN 2349-2317 (Online); DOI: 10.16962/EAPJMRM/issn. 2349-2317/2015; Volume 8 Issue 1 (2017)

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ARIMA/GARCH (1,1) MODELLING AND FORECASTING FOR A GE STOCK

PRICE USING R

Varun Malik Dyal Singh College University of Delhi India varunmalikphy@

ABSTRACT

This article attempts to present a basic method of time series analysis, modelling and forecasting performance of ARIMA, GARCH (1,1) and mixed ARIMA - GARCH (1,1) models using historical daily close price downloaded through the yahoo finance website from the NASDAQ stock exchange for GE company (USA) during the period of 2001 to 2014. This paper also presents a brief analysis technique introduction to R to build up graphing, simulating and computing skills to enable one to see models in economics in a unified way. The great advantage of R compiler is that it is free, extremely flexible and extensible. It uses data that can be downloaded from the internet, and which is also available in different R packages. This article provides discuses in modeling and forecasting briefly and simply. This paper provides short details the R command lines and output. This article is written to be useful for learning time series analysis on basic different levels as well as a research purpose for beginners who beginning the analysis of time series data in the various scientific and statistical research approaches. ARIMA/GARCH (1,1) model is applied to observed the forecasting values of low and high stock price (in USD) for GE company. The results obtained in this paper are based on the work of [10].

Keywords: ARIMA/GARCH models, time series models, forecasting, R

INTRODUCTION In time series are analyzed to understand behavior of the past data points and to predict the future values on the basis of past values, enabling analysis's or decision makers to make properly informed decisions for others. A time

series analysis quantifies the main observation findings from data and the random variable. This reason, combined with improved computing, technical and statistical ideas, have made time series methods widely applicable in scientific and statistical research approach in

ELK ASIA PACIFIC JOURNAL OF MARKETING AND RETAIL MANAGEMENT

ISSN 2349-2317 (Online); DOI: 10.16962/EAPJMRM/issn. 2349-2317/2015; Volume 8 Issue 1 (2017) ...............................................................................................................

governments and private sectors. In most branches of scientific and statistical research department in private and government sectors, there are variables measured approaches sequentially in time. Financial/Banking sector record interest rates as well as exchange rates each day. The government statistics department compute and analyze the country's GDP on a yearly basis and other economic data. The weather department publishes day to day temperatures and air velocity diagram for capital cities and in rural areas from around the world. Meteorological department record weather parameters at many different sites with different instrument such as Weather radar and optical rain gauge meter and etc. When such variable is measured sequentially in time over or at a regular interval, known as the sampling interval, the resulting data come from a time series. Observations that have been collected over regular sampling intervals from a historical time series. In this paper, we give a basic but useful computational and statistical approach in which the historical stock price series are treated as realizations of sequences of random variables.

A sequence of random variables published at regular sampling intervals is sometimes referred to as a discrete-time stochastic process, though the shorter name time series model is often preferred. The theory of stochastic processes is vast and may be studied without necessarily fitting any models over time series data. However, our aim is to more applied and directed towards model fitting and forecasting the data using R computational techniques. The main features of various time series are to detect the trends and seasonal variations that can be modelled deterministically with respect to mathematical functions of time. But, another important feature of most of the time series is that observations close together in time tend to be correlated. Some of the methodology in a time series analysis is focused on explaining this correlation factor and the main features in the data using appropriate statistical models and descriptive methods. Once an accurate model is observed and fitted to data values, then researcher used the model to forecast future values, or generate simulations, to guide planning decisions and future prediction. Fitted

ELK ASIA PACIFIC JOURNAL OF MARKETING AND RETAIL MANAGEMENT

ISSN 2349-2317 (Online); DOI: 10.16962/EAPJMRM/issn. 2349-2317/2015; Volume 8 Issue 1 (2017) ...............................................................................................................

models are also used as a basis for

statistical tests.

Finally, a fitted statistical model provides

a concise and informative summary of

the main characteristics of a time series,

which can often be essential for

researcher and scientists and financial

analysis. Sampling intervals may be

differ in their relation to the data. The

data may have been aggregated (for

example, the number of foreign

passengers reaching per day/month/year)

or sampled (as in a daily/weekly/monthly

basis time series of trade share prices). If

data are sampled, the sampling interval

must be short enough for the time series

to provide a very close approximation to

the original continuous signal when it is

interpolated. In a volatile share market,

close of historical prices may not suffice

for interactive trading but will usually be

adequate to show the nature of trends

and movement of the stock market price

over several years [1] [2] [3]

The objective of this paper is to provide

a procedure of modelling and

forecasting method in terms of

ARIMA/GARCH

modelling for

researchers by means of statistical R

applications. Furthermore, we have

shown how to use R to find these stock

price prediction. We begin with some basic thoughts about how to store and process time series data using R software.

Despite the fact that the auto regressive integrated moving average (ARIMA) technique is powerful and flexible also but it is not able to handle the volatility and nonlinearity that are present in the data series. Some previous studies showed that generalized autoregressive conditional heteroskedatic (GARCH) models are used in time series forecasting to handle volatility in the data series. [5][6][8].

In the next section we will discuss the methodology and data preparation. In particular, Time series and R analysis packages have been discussed in brief in sections 3, we have discussed stationary, non stationary and estimation of linear trend (GLM) and ACF and PACF plots respectively in section 4. Then, in section 5, selection of ARIMA model and in section 6 GARCH (1,1) have been discussed. In section 7, we have obtained the ARIMA/ GARCH (1,1) model performance for GE stock price. Finally, we conclude this paper in section 8.

ELK ASIA PACIFIC JOURNAL OF MARKETING AND RETAIL MANAGEMENT

ISSN 2349-2317 (Online); DOI: 10.16962/EAPJMRM/issn. 2349-2317/2015; Volume 8 Issue 1 (2017) ...............................................................................................................

METHODOLOGY AND DATA

IT is assumed that you have installed R software on your computer/laptop or machine, and it is suggested that you work through the examples, making sure your output agrees with the results. If you do not have R, then it can be installed free of charge from the Internet site r-. It is also recommended that you have some familiarity with the basics statistical packages of R, [1].

In this analysis, we used some of the time series and forecasting packages such as zoos, xts, ts, astsa, fts, and forcast. For representing irregularly spaced time series, the packages timeSeries, zoo and xts are mostly used in time series analysis. In these packages, timeSeries objects are the core data objects. But this timeSeries objects are not frequently used as zoo and xts objects for representing time series data. A very flexible time series class is zeileis ordered observations (zoo) created by Achim Zeileis and Gabor Grothendieck and available in the package zoo on CRAN , [1][10][11][12].

In this study, A Regularly spaced time series structure, data are arranged with a

fixed interval of time, can be represented

as under the packages ts. we used

historical stock price data over the

period 2001 to 2015 and stored the data

in the .csv file .The function read.csv()

comes to read data from .csv file which

stored on your computer and laptop .

Notice that the first row contains the

names of the columns namely Date, the

date information is in the first column

with the format dd/mm/YYYY, stock

price in the second column namely close

.The first step of identification is to check

the occurrence of a trend in data series

movement by plotting time series which

is as shown in Figure 1 . From the

plotting, it can be seen that the data time

series does not vary in a fixed level or

not which indicates that the series is non

stationary and stationary in both mean

and variance, as well as exhibits an

nature of trends. Time series are shown

in figure 1 as well as figure 2.

General Electric ,GE, is an

American multi

national company

incorporated in New York USA. The

company operates through the following

segments i.e., Power & Water, Oil and

Gas, Aviation, Healthcare, Transportatio

n and Capital which cater to the needs of

services, Medical

devices, Life

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ISSN 2349-2317 (Online); DOI: 10.16962/EAPJMRM/issn. 2349-2317/2015; Volume 8 Issue 1 (2017) ...............................................................................................................

Sciences, Pharmaceutical, Automotive, S oftware Development and Engineering industries , [1][10][11][12]. (Refer Fig. 1)

WORKING WITH TIME SERIES DATA The native R classes suitable for storing time series data include vector, matrix , data.frame, and ts objects. But the types of data that can be stored in these objects are narrow; furthermore, the methods provided by these representations are limited in research and analysis scope. There exist specialized objects that deal with more general representation of time series data as zoo, xts, or time Series objects, available from packages of the same name. It is not necessary to create time series objects for every time series analysis problem, but more sophisticated analyses require time series objects. You could calculate the mean or variance of time series data represented as a vector in R, but if you want to perform a seasonal decomposition using decompose, you need to have the data stored in a time series object. .[1][10][11][12] In the following examples, we assume you are working with zoo,ts forcast,timeseries ,stats objects and etc.

because we think there are the most widely used packages. Before using statistical objects in r software, we need to install and load the appropriate statistical and forcasting package (if you have already installed it, you only need to load it) using the appropriate command, [1][2][3][9].

ESTIMATING A LINEAR TREND Consider the Stock price series is shown in Figure 2.The data are mean stock close price index from 2001 to 2014. In particular data are deviations , measured in USD. We note that an apparent upward trend in the series during this period. A simple kind of generated series might be a collection of uncorrelated random variables, wt with mean 0 and finite variance 2w. The time series generated from uncorrelated variables is used as a model for noise in statistical research purpose, where it is called white noise; The designation white originates from the analogy with white light and indicates that all possible periodic oscillations are present with equal strength. Now We express simple linear regression to estimate that trend by fitting the model over time series xt = 1 + 2t + wt,t =

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