arima - asjp.cerist.dz

2021

75

ARIMA Forecasting Foreign Exchange Reserves Using ARIMA Model

(Algeria Case for 1969-2022)

[email protected]@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 [email protected]

mailto:[email protected]

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)

.


(Balogh, 1960, p. 372) -

.

(Balogh, 1960, p. 368) (Heller, 1966, p. 296)


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



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


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 -4.9837 Prob. 0.0000 Prob. 0.0000

Eviews 12

ARIMA I=1 AR MA

:ARIMA :

Date: 06/18/21 Time: 15:27


Included observations: 50 after adjustments


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


Q-statistic probabilities adjusted for 13 ARMA terms


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).

https://www.data.worldbank.org/

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