Forecasting Turkish lira against the US Dollars via forecasting approaches

Figures & data

Table 1. Assessment of explanatory variables

Variables name	Variable	Assessment
Money supply	MS	Stock of money
Interest rate	IR	Rate of central bank
Inflation	INF	Consumer price index
GDP-Real	GDP	IPI
Trade balance	TB	Exports, imports
Foreign reserves	FR	Official foreign reserves
Oil price	OP	Price of crude oil

Table 2. Unit root test—explanatory variables

Variables	Augmented dickey- fuller test		Phillip peron test
	Level	1^st diff	Level	1^st diff
FE	–2.067151	–9.790111	–1.942644	–10.45724
FR	–1.980402	–11.37819	–1.980402	–11.37819
GDP	–1.571611	–1.899766	–9.752516	–
MS	–5.014965	–	–2.805490	–8.559155
INF	0.593596	–6.140452	0.338016	–7.615172
IR	–3.200127	–3.335820	–2.352380	–10.05454
TB	–	–14.61663	–5.171394	–17.47622

Table 3. ARIMA statistics

Models	Selected models	R-Squared		Akaikeinfo		Schwarz criterion
ARMA/ARIMA	ARIMA(2,2)	0.014586		–0.348285		–0.248366
Exponential smoothing	Trend	α	β	Ø	γ	A.I.C
		1.0000	0.000	----	0.000	70.06440

Table 4. Coefficients of NARD long run

Variables	Probability	Standard error	T-Statistics
FR-POS	0.1090	3.26E-06	–1.629725
FR_NEG	0.1041	2.86E-06	–2.537572
OP_POS	0.4251	0.002963	0.809914
OP_NEG	0.4579	0.747629	0.4579
TB_POS	0.5508	7.37E-06	0.600274
TB_NEG	0.5730	7.49E-06	–0.567076
GDP_POS	0.0564	0.000879	1.949403
GDP_NEG	0.3344	0.000664	–0.973975
GP-POS	0.8056	0.000191	–0.247299
GP_NEG	0.9692	0.000234	0.038831
F-Statistics	3.459068	R-Squared	0.996567
Bound test	3.459063	l0 Bound: 3.350	l1 Bound 2.620
Diagnostic tests		P Value
The Breusch-Godfrey serial correlation LM test		0.5751
The heteroskedasticity test: Harvery		0.1056
The RESET test		0.1187

Table 5. Results of combined models via equal weights and var-cor approaches

ARIMA	Naïve	Exponential Smoothing	NARDL	ANN
4.506	1.8522	4.563	1.390	1.454
	Two-Way Combinations (EW)
AR-ES	AR-N	AR-ND	ES-N	ES-ND
4.534	3.179	2.948	3.207	2.976
AR-ANN	ES-ANN	ND-ANN	N-ANN	N-ND
2.333	1.325	1.333	0.999	1.6211
Three-Way Combinations (EW)
AR-ES-N	AR-ES-ND	ES-N-ND	AR-N-ND	AR-ES-ANN
3.64	3.486	2.601	1.398	1.236
AR-N-ANN	ES-N-ANN	AR-ND-ANN	N-ND-ANN
2.666	3.565	2.222	2.008
Four-Way Combination (EW)			Five-Way Combination (EW)
AR-ES-N-ND	AR-ES-N-ANN	ES-N-ND-ANN	AR-ES-N-ANN
3.64	3.486	2.601	0.8888
	Two-Way Combinations (VC)
AR-ES	AR-N	AR-ND	ES-N	ES-ND
2.342	1.076	1.253	1.218	1.388
AR-ANN	ES-ANN	ND-ANN	N-ANN	N-ND
1.222	1.085	0.764	0.854	0.764
Three-Way Combinations (VC)
AR-ES-N	AR-ES-ND	ES-N-ND	AR-N-ND	AR-ES-ANN
1.638	1.577	1.089	0.987	0.999
AR-N-ANN	ES-N-ANN	ES-N-ND	N-ND-ANN
1.086	1.247	1.089	1.585
Four-Way Combination (VC)			Five-Way Combination (VC)
AR-ES-N-ND	AR-ES-N-ANN	ES-N-ND-ANN	AR-ES-N-ANN
1.232	1.229	0.969	0.854

AR = Autoregressive Distributive Lag Model, N = Naïve, ND = NARDL Model, ES = Exponential Smoothing Model, ANN = Artificial Neural Network, VC = Var-Cor Approach, EW = Equal-Weights Approach.

Figure 1. CUSUM and CUSUMQ-NARDL.