SPSS Coursework: Analysis of EUR/USD Exchange Rate Data and Models

This document presents an analysis of EUR/USD exchange rates using SPSS, focusing on descriptive statistics and time series modeling techniques. The analysis begins with an introduction to time series methods and their importance in prediction, particularly within the context of currency exchange rates. Descriptive statistics, including measures of central tendency, dispersion, and skewness, are computed to provide an initial understanding of the data's characteristics. The analysis then proceeds to apply ARCH and GARCH models to forecast currency exchange rate movements. ARIMA modeling is also employed, with detailed results presented, including goodness-of-fit statistics, parameter values, and residual analysis. The document includes ACF and PACF plots and discusses their role in time series prediction. The conclusion emphasizes the significance of time series methods for business firms and the benefits of using time series modeling for analysts, offering valuable insights into financial forecasting. The document is a student's assignment, available on Desklib, a platform offering AI-based study tools.

SPSS COURSWORK DATA
ANALYS, DESCRIPTIVE
STATISTIC EUR/USD

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
Analysis...........................................................................................................................................1
ARCH model...............................................................................................................................2
GARCH.......................................................................................................................................9
CONCLUSION..............................................................................................................................11
REFERENCES..............................................................................................................................12
.......................................................................................................................................................12

INTRODUCTION
Time series is the one of the most important method that is used to make prediction. In current report GARCH and ARCH
model is applied to make prediciton about currency exchange rate. Apart from this, in order to develop broad understanding about
topic descriptive analysis method is applied on data set and in this data analysis of currency exchange rate is done.
Analysis
Descriptive Statistics
N Minimum Maximum Mean Std. Deviation Skewness
Statistic Statistic Statistic Statistic Statistic Statistic Std. Error
Currencyexchangerate 777 1.04 1.39 1.1483 .09237 1.295 .088
Valid N (listwise) 777
Mean value of currency is 1.14 which is indicating that on average basis currency value remain 1.14 in the market. Standar deviation
value is only 0.09 which is indicating that values are deviating at low pace in data set. There is huge difference between mean and
maximum as well as minimum value and this reflect that currency heavily fluctuate in past time period.
Statistics
Currencyexchangerate
N Valid 777
Missing 0
Skewness 1.295
Std. Error of Skewness .088
Skewness value is 1.295 which is indicating that data is not normally distributed. Hence, linear models cannot be applied on data set.
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ARCH model
Summary statistics:
Variable
Ob
ser
vat
ion
s
Obs.
with
missin
g data
Obs.
without
missing
data
Minim
um
Maxim
um Mean
Std.
deviati
on
1.3867
77
5 0 775 1.039 1.393 1.148 0.092
Results of ARIMA modeling of the 1.3867 series:
Results after optimization (1.3867):
Goodness of fit statistics:
Observations
77
5
DF
77
3
SSE
0.0
32
92
1
MSE
4.2
5E
-05
RMSE 0.0
06
51
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8
WN Variance
4.2
5E
-05
MAPE(Diff)
0.4
27
57
4
MAPE
0.4
27
57
4
-2Log(Like.)
-
55
91.
69
FPE
4.2
6E
-05
AIC
-
55
87.
69
AICC
-
55
87.
68
SBC
-
55
78.
39
Iterations 1
Model parameters:
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Parameter
Va
lue
Hessia
n
standar
d error
Lower
bound
(95%)
Upper
bound
(95%)
Constant
0.0
00 1.244 -2.439 2.439
Parameter
Va
lue
Hessia
n
standar
d error
Lower
bound
(95%)
Upper
bound
(95%)
Asymp
t.
standar
d error
Lower
bound
(95%)
Upper
bound
(95%)
AR(1)
1.0
00 0.000 1.000 1.000 0.000 1.000 1.000
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D
es
cr
ip
ti
v
e
a
n
al
ys
is
(
R
es
id
u
al
s)
:
ASL U P S L U
10 1 0
- 0- 0 - 0 - 0
00- 0 0 0 - 0
- 0- 0 - 0 - 0
00- 0 0 0 - 0
00- 0 0 0 - 0
- 0- 0 - 0 - 0
00- 0 0 0 - 0
00- 0 0 0 - 0
- 0- 0 - 0 - 0
- 0- 0 - 0 - 0
00- 0 0 0 - 0
00- 0 0 0 - 0
- 0- 0 - 0 - 0

0 100 200 300 400 500 600 700 800
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
ARIMA (1.3867)
1.3867 ARIMA (1.3867)
Prediction Lower bound (95%)
Upper bound (95%)
Time step
1.3867
GARCH
Uncondition
al Variance
0.0009636
9
ω
0.0000039
7
α
0.0824292
2
β
0.8740566
4
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7/5/2014
4/11/2014
6/5/2015
3/11/2015
5/5/2016
2/11/2016
0.0000
0.0500
0.1000
0.1500
0.2000
0.2500
0.3000
0.3500
Conditionaland Unconditional EUR/USD
Exchange Rate Volatility
Date
Standard Deviation
ACF and PACF plots are one of the important tool that are used to make predicition. ACF refers to autocorrelation and PACF refers to
partial autocorrelation. There is great use of both apporahces as same are used to make prediction. ARCH and GARCH are commonly
used approaches in time series modeling. It can be seen from chart that in ACF chart there is spike in first lag and latter spikes are
below dotted line. This reflects that there is feature of stationary in data set (Sample ACF and Properties of AR(1) Model, 2017). While
making prediction it is very important to ensure that analyzed data is stationary in nature. In case there will not be stationary feature
then prediction of accurate level can not be made. This is because time series is imapcted by seasonal and cyclical factors. In
application of ARCH model these factors are removed from data set. This ensured that there is heavy reliability of time series model.
Chart that is in GARCH model is reflecting that in future also exchange rate will remain stable around mean value as it can be seen
that there is little spike in chart and in rest of part there is stability in part. Standard deviation is nearly 0.05 which clearly stated that
values will not deviate at fast pace. Hence, it is predicted that currency will move around its mean value in upcoming time period.
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CONCLUSION
On the basis of above discussion it is concluded that there is significent importance of time series method for the business
firms because by using same accurate prediction can be made about future time period. ARIMA is commonly model that is applied for
time series analysis. ACF and PACF charts help one in making prediction in appropriate manner by using time seris chart. It can be
said that there are number of benefits that are dervived by analysts by making use of time series modeling.
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REFERENCES
Online
Sample ACF and Properties of AR(1) Model, 2017. [Online]. Available
through:<https://onlinecourses.science.psu.edu/stat510/node/60>. [Accessed on 29th September 2017].
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