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2021
75
ARIMA Forecasting Foreign Exchange Reserves Using ARIMA Model
(Algeria Case for 1969-2022)
1m.cherfaoui@univ-dbkm.dzk.bekkouche@univ-dbkm.dz
.
ARIMA
JELC22C32C51C52C53C61
Abstract:
This study tries to estimate a standard model that can predict foreign exchange reserves in
Algeria for the next three years until 2022, through the use of annual data from the World Bank
database for the period from 1969 to 2019, were applied the autoregressive and moving averages
model at the first differencing degree.
On the theoretical side, the study concluded that the depletion of reserves will be by the end of
2022 with no changes in oil prices, while the estimated ARIMA model results its predictions more
optimistic, as it expected the growth of reserves again starting from 2020 to reach $120.7 billion by the
end of 2022.
Keywords: foreign exchange reserves, autoregressive, moving averages, ARIMA model, forecasting.
JEL Classification Cods : C22, C32, C51, C52, C53, C61.
1 m.cherfaoui@univ-dbkm.dz
58
.
(worldbank, 2021)
. :
(ARIMA)
(ARIMA)
ARIMA
59
3
. ARIMA
.
60
:-.-ARIMA
-:
(Worrell, 1976, p. 260)
.
(Heller, 1966, p. 297). . (Williamson, 1973, p.
687) : -
(Heller, 1966, p. 305).
(Heller, 1968, p. 142).
(Heller, 1968, p. 142).
ARIMA
61
.
:
.
.-
.
62
.
. (Williamson, 1973, p. 700)
.
(Williamson, 1973, p. 722)
.
(Williamson, 1973, p. 722)
(Balogh, 1960, p. 372) -
.
(Balogh, 1960, p. 368) (Heller, 1966, p. 296)
(Williamson, 1973, p. 704)
ARIMA
63
.
(Heller, 1966, pp. 296-297). :
.:
-
- .
.
.
(Heller, 1966, p. 305) (Worrell ,1976, p. 260)
.
(Heller, 1966, p. 300)
64
(Heller, 1966, p. 301)
(Heller, 1966, p. 301)
(Heller, 1968, p. 141) Worrell, 1976, p. 260)
(Balogh, 1960, p. 364)
(Heller, 1966, p. 299) (Clark, 1970, p. 357)
. (Hipple, 1975, p. 628)
. (Agarwal, 1971, pp. 77-78)
:
(Balogh, 1960, p. 363)
ARIMA
65
(Balogh, 1960, p. 262) ( Worrell, 1976,
p. 261)
:
148 2008 4.16 1995 1969 155 2009 6.30 1996 4.01 1983 1970 170 2010 6.67 1997 3.19 1984 1971 191 2011 8.45 1998 4.64 1985 1972 20 2012 6.15 1999 3.84 1986 1973 2013 13.6 2000 4.34 1987 1974
15.4 186 2014 19.6 2001 3.19 1988 1975 35 151 2015 25.2 2002 3.09 1989 1976 30 121 2016 35.5 2003 2.70 1990 1977 16 105 2017 45.7 2004 3.46 1991 1978
17.6 87.4 2018 59.2 2005 3.32 1992 1979 15.6 71.8 2019 81.5 2006 3.66 1993
115 2007 4.81 1994 2021
66
.
.
. -
ARIMA :
ARIMA
67
Date: 06/18/21 Time: 15:13
Sample (adjusted): 1970 2019
Included observations: 50 after adjustments
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
1 0.819 0.819 35.593 0.000
2 0.585 -0.260 54.140 0.000
3 0.440 0.159 64.830 0.000
4 0.244 -0.369 68.183 0.000
5 0.050 0.025 68.325 0.000
6 -0.098 -0.185 68.889 0.000
7 -0.272 -0.219 73.356 0.000
8 -0.399 0.010 83.204 0.000
9 -0.388 0.138 92.756 0.000
10 -0.328 0.051 99.729 0.000
11 -0.312 -0.167 106.23 0.000
12 -0.273 0.007 111.31 0.000
13 -0.200 -0.067 114.11 0.000
14 -0.144 -0.027 115.60 0.000
15 -0.118 -0.212 116.63 0.000
16 -0.072 0.104 117.03 0.000
17 -0.040 -0.041 117.16 0.000
18 -0.052 -0.056 117.38 0.000
19 -0.045 -0.034 117.55 0.000
20 -0.018 -0.014 117.58 0.000
21 -0.021 -0.003 117.62 0.000
22 -0.028 -0.114 117.70 0.000
23 -0.017 -0.026 117.72 0.000
24 -0.018 -0.053 117.76 0.000
Eviews 12
. ARIMA
ADF PP
:
Eviews 12
:
UNIT ROOT TEST TABLE (PP) UNIT ROOT TEST TABLE (ADF) At Level
FXR FXR With Constant t-Statistic -1.3165 With Constant t-Statistic 3.8520 Prob. 0.6149 Prob. 1.0000 With Constant & Trend t-Statistic -1.8450 With Constant & Trend t-Statistic 2.3304 Prob. 0.6677 Prob. 1.0000 Without Constant & Trend
t-Statistic -0.8647 Without Constant & Trend
t-Statistic 4.3373 Prob. 0.3364 Prob. 1.0000
At First Difference d(FXR) d(FXR) With Constant t-Statistic -2.0018 With Constant t-Statistic -0.2398 Prob. 0.2852 Prob. 0.9246 With Constant & Trend t-Statistic -1.9858 With Constant & Trend t-Statistic -5.4554 Prob. 0.5944 Prob. 0.0003 Without Constant & Trend
t-Statistic -2.0417 Without Constant & Trend
t-Statistic 0.4626 Prob. 0.0406 Prob. 0.8100
68
UNIT ROOT TEST TABLE (PP) UNIT ROOT TEST TABLE (ADF) At Level
LFXR LFXR With Constant t-Statistic -1.5251 With Constant t-Statistic -1.5993 Prob. 0.5128 Prob. 0.4755 With Constant & Trend t-Statistic -1.4637 With Constant & Trend t-Statistic -4.7774 Prob. 0.8289 Prob. 0.0020 Without Constant & Trend
t-Statistic 1.8796 Without Constant & Trend
t-Statistic 2.4332 Prob. 0.9844 Prob. 0.9959
At First Difference d(LFXR) d(LFXR) With Constant t-Statistic -5.6166 With Constant t-Statistic -5.5046 Prob. 0.0000 Prob. 0.0000 With Constant & Trend t-Statistic -5.7934 With Constant & Trend t-Statistic -5.6948 Prob. 0.0001 Prob. 0.0001 Without Constant & Trend
t-Statistic -5.1929 Without Constant & Trend
t-Statistic -4.9837 Prob. 0.0000 Prob. 0.0000
Eviews 12
ARIMA I=1 AR MA
:ARIMA :
Date: 06/18/21 Time: 15:27
Sample (adjusted): 1970 2019
Included observations: 50 after adjustments
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
1 0.208 0.208 2.3014 0.129
2 0.114 0.074 3.0094 0.222
3 0.146 0.114 4.1843 0.242
4 0.057 0.001 4.3684 0.358
5 0.109 0.082 5.0506 0.410
6 0.261 0.222 9.0843 0.169
7 0.085 -0.017 9.5243 0.217
8 -0.166 -0.258 11.234 0.189
9 -0.108 -0.119 11.974 0.215
10 -0.295 -0.296 17.613 0.062
11 -0.078 0.031 18.017 0.081
12 -0.168 -0.201 19.955 0.068
13 -0.206 -0.114 22.950 0.042
14 -0.200 -0.029 25.836 0.027
15 -0.192 0.013 28.577 0.018
16 -0.191 0.021 31.363 0.012
17 -0.128 -0.022 32.652 0.012
18 -0.075 -0.035 33.107 0.016
19 -0.281 -0.239 39.733 0.004
20 -0.018 0.003 39.760 0.005
21 -0.015 -0.017 39.781 0.008
22 -0.077 -0.167 40.332 0.010
23 0.077 0.032 40.903 0.012
24 0.082 0.016 41.580 0.014
Eviews 12
AR MA :
ACF MA = PACF AR =. ARIMA
ARIMA
69
MA = AR =10 I=1 :
ARIMA (ARmax=10, I=1, MAmax=10) ARIMA Eviews 12
: ARIMA
Dependent Variable: D(LFXR) Method: ARMA Maximum Likelihood (BFGS) Date: 06/18/21 Time: 15:36
Sample: 1970 2019 Included observations: 50 Convergence achieved after 137 iterations Coefficient covariance computed using outer product of gradients d.f. adjustment for standard errors & covariance R-squared 0.694438 Mean dependent var 0.103278 Adjusted R-squared 0.572213 S.D. dependent var 0.282878 S.E. of regression 0.185018 Akaike info criterion 0.119888 Sum squared resid 1.198102 Schwarz criterion 0.693495 Log likelihood 12.00280 Hannan-Quinn criter. 0.338321 F-statistic 5.681637 Durbin-Watson stat 1.947969 Prob(F-statistic) 0.000015 Inverted AR Roots .98-.21i .98+.21i .45+.78i .45-.78i
-.12 -.47+.76i -.47-.76i -.92+.32i -.92-.32i
Inverted MA Roots 1.00-.07i 1.00+.07i -.89+.46i -.89-.46i Eviews 12
ARIMA ( AR=9, I=1, MA=4) Akaike :
.10
.12
.14
.16
.18
.20
.22
(9,4)(
0,0)
(9,5)(
0,0)
(11,3)
(0,0)
(7,3)(
0,0)
(10,4)
(0,0)
(8,3)(
0,0)
(11,4)
(0,0)
(8,6)(
0,0)
(8,8)(
0,0)
(8,1)(
0,0)
(10,2)
(0,0)
(10,1)
(0,0)
(10,6)
(0,0)
(12,1)
(0,0)
(8,4)(
0,0)
(10,5)
(0,0)
(10,3)
(0,0)
(10,7)
(0,0)
(9,3)(
0,0)
(9,8)(
0,0)
Akaike Information Criteria (top 20 models)
Eviews 12
70
R2 Adju .
.
:
Date: 06/18/21 Time: 15:44
Sample (adjusted): 1970 2019
Q-statistic probabilities adjusted for 13 ARMA terms
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
1 0.001 0.001 2.E-05
2 0.010 0.010 0.0057
3 0.097 0.097 0.5223
4 0.001 0.001 0.5224
5 -0.043 -0.045 0.6274
6 -0.132 -0.143 1.6542
7 0.022 0.023 1.6835
8 -0.003 0.010 1.6840
9 -0.263 -0.243 6.0636
10 -0.067 -0.082 6.3559
11 -0.165 -0.187 8.1657
12 -0.189 -0.189 10.614
13 -0.064 -0.080 10.906
14 -0.024 -0.048 10.946 0.001
15 0.067 0.002 11.280 0.004
16 0.114 0.104 12.271 0.007
17 0.151 0.131 14.060 0.007
18 0.069 -0.016 14.447 0.013
19 0.006 -0.043 14.451 0.025
20 0.090 -0.012 15.154 0.034
21 0.135 0.058 16.799 0.032
22 -0.139 -0.210 18.583 0.029
23 0.050 -0.049 18.819 0.043
24 0.087 0.020 19.573 0.052
Eviews 12
.
Heteroskedasticity ARCH :
ARIMA
71
Heteroskedasticity Test: ARCH F-statistic 2.072362 Prob. F(1,47) 0.1566 Obs*R-squared 2.069306 Prob. Chi-Square(1) 0.1503
Eviews 12
.
Jarque-Bera :
0
2
4
6
8
10
-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4
Series: Residuals
Sample 1970 2019
Observations 50
Mean -0.000183
Median 0.008165
Maximum 0.422820
Minimum -0.429068
Std. Dev. 0.156368
Skewness -0.334739
Kurtosis 3.616171
Jarque-Bera 1.724724
Probabil ity 0.422164
Eviews 12
Jarque-Bera .
Eviews 12
:
72
-.6
-.4
-.2
.0
.2
.4
.6
-0.4
0.0
0.4
0.8
1.2
70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
Eviews 12
.
:
Eviews 12
ARIMA(9,1,4)
ARIMA
73
0.0E+00
4.0E+10
8.0E+10
1.2E+11
1.6E+11
2.0E+11
2.4E+11
70 75 80 85 90 95 00 05 10 15 20
FXR_2024 FXR Eviews 12
-
ARIMA
-
-
74
-
ARIMA
-
-
ARIMA
75
-
-
-
-
-
Agarwal, J. P. 1971, Optimal Monetary Reserves for Developing Countries,
Weltwirtschaftliches Archiv, 76-91.
Balogh, T, 1960, International Reserves and Liquidity, The Economic Journal, 357-
377.
Clark, P ,1970, Optimum International Reserves and the Speed of Adjustment,
Journal of Political Economy, 356-376.
76
Heller, H, 1966, Optimal International Reserves, Royal Economic Society, 296-311.
Heller, H, 1968, The Transactions Demand for International Means of Payments.
Journal of Political Economy, 141-145.
Hipple, F, 1975, The Adequacy of International Reserve Stocks: An Empirical Study,
Southern Economic Journal, 627-634.
Kelly, M. G, 1970, The Demand for International Reserves, The American Economic
Review, 655-667.
Williamson, J, 1973, Surveys in Applied Economics: International Liquidity, The
Economic Journal, 685-746.
Worrell, D, 1976, The Theory of Optimal Foreign Exchange Reserves in A
Developing Country, Social and Economic Studies, 259-279.
Worldbank, 2021, data.worldbank, Retrieved from https://www.data.worldbank.org,
visited (03 19,2021).
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