Tenge exchange rate model using new neural network training
method
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Abstract: The paper reports results derived from new robust neural network (RNN) based
KZT/USD exchange rate model against AR (2) model. The characteristic of the RNN method
is explained followed by comparative study of quarterly KZT/USD models. Diagnostic
measure such as mean absolute deviations (MAD), R2 and tracking signals (TS) suggests
superiority of the RNN KZT/UDS model. The RNN training methods computes adoptive
directional search vectors such that the error function is gradually optimized. The method
automatically computes adjustable dynamic learning rates to direct search toward the
minimum valley of the error function. The algorithm identifies dynamic adjustable learning
rates to generate convergent sequence of the error function. As a result, the training is robust
to model exchange rate. The RNN model performs better in MAD, TS and R2 value.
Key-Words- KZT/USD Exchange rate, Robust Neural Networks, Adjustable training,
Forecast.
1. Introduction
Due to the exchange rate crisis in the CIS region during the fall of USSR era, many small
open economies have adopted flexible exchange rates in combination with some kind of
monetary or interest rate mechanism. Volatility of exchange rate in Kazakhstan is significant
issue taking account possibility of huge transaction loss induced by volatility exchange rate.
Kazakhstan economy highly depends on international trade and FDI (Foreign Direct
Investment), exchange rate volatility in Kazakhstan have influence in international trade and
FDI. Kazakhstan has consistently achieved moderate growth rate induced by oil export. But
international oil price is declining and under such market condition exchange rate could be
influenced by several possible macroeconomic factors. USD (dollar) exchange rate trends had
grown up to 2003 but dollar’s exchange rate to Tenge has fallen since 2003 (see Table 1).
There have been number of attempts to apply neural network (NN) to the task of financial
modeling (Cao et al. 2005, Jasic and Wood 2004, Kaastra and Boyd 1995, Lam 2004, Nygren
2004). When it comes to performing a predictive analysis, it is very difficult to build one
general model that will fit every market. Such models tend to be specific to markets and asset
classes and a general model may not be applicable across markets. Similarly, there may be
some temporal changes as well which mean that the models may need to be modified over
time in order to preserve their effectiveness (Zhang, et al, 1998). We develop KZT/USD
exchange rate forecast model using new RNN training method and brief results are reported
to show the superior performance of the model, against AR (2) model.
2 Rationales for Self-Adaptive Training Method
Consider a NN error function with m training weights and the learning rates are identified
m
automatically. For computational convenience, the higher dimensional error function in E
dimension is decomposed into several error functions in lower dimension. Such transformed
error function retains the true convex characteristics of the original error function. The
gradient information is evaluated and the training method updates all the network weight
parameters say wj, j=1,2,…..m, by a factor such that improvement in training is noticed. Each
epoch identifies m different learning rates along the training directions. Once the NN training
weights are updated, the error function is evaluated to notice the improvement in error
function and the rate of convergence. Various form of standard back propagation training
method and its variant are not self-adaptive. They are heuristic training method (Ahmed et al
2000a; Haykin, 1999; Weir, 1991; and Kamarthi et al., 1999). The training direction, d k of
the error function f (w) is computed using the gradient, ▽f (wk) information from a single
training pattern in standard on-line back propagation (Bishop, 1995, Ahmed, et al, 2000b).
The fixed value of a learning rate,  k does not always lead to a maximum local decrease in
function value. The learning rate depends on the shape of the error function (Jacobs, 1988) as
it trains from the current epoch k to the next epoch k+1, k+2,… and so on. The constant
value of learning rate, η k , can direct the search away from the local minimum during epoch k
and the directions dk generated from gradient ▽f (wk) are different for a single weight
component in standard back propagation training. Consider a training method, we call RNN,
where an iterative algorithm is applied to an error function with an initial arbitrary weight
vector wk, at the beginning of iteration k, the algorithm generates a sequence of vectors w k+1,
w k+2,.… during epoch k+1, k+2,….,.., and henceforth. The iterative algorithm is globally
convergent if the sequence of vectors converges to a solution set Ω. Consider the problem:
minimize f (w), subject to: w Є Em. Let, Ω Є Em be the solution set, and let, the application of
an algorithmic map, ℬ, generates the sequence w k+1, w k+2,.…, starting with weight vector wk
such that (w k, w k+1 , w k+2,.…) Є Ω, then the algorithm converges globally and the algorithmic
map is closed over Ω. The following properties are utilized to train the new RNN.
Property 1: Suppose that f: E m → E1 and the gradient of the error function, ▽f (w), is
defined then there is a directional vector d such that ▽f (w)T d < 0, and f(w +ηd) < f(w) : (η
Є (0,  ),  > 0), then the vector d is a descent direction of f (w), where  is assumed arbitrary
positive scalar.
Property 2: Let f: E m → E1 is a descent function. Consider any training weight w Є Em and
d Є Em : d ≠0. Then the directional derivative ▽f(w, d) of the error function f(w) in minimum
direction d always exists. The expression to update the RNN network weight, wk+1 is given by
w k+1 =w k + ηk dk. Here, η k is defined as a minimization problem of the type: η k = {min f(w +
ηd)}; subject to : ηk Є L, where, L = (η : η Є E1).
3. Results
The following table shows R2 as well the MAD value for the RNN model is better than the
AR (2) model. This confirms the superiority of the KZT/USD exchange model using the new
RNN method. The TS vale in both case are within acceptable limits, however, the plot shows
that the TS vale in RNN is asymmetrical on the zero level, hence the overall predictability is
good with RNN model.
Mode
l
RNN
R2
0.9
2
MA
D
3.11
TS
0.05
1
TS Plot
Fitted & Actual Data
TS= ∑E/MAD
6.00
100.00
7 9 11 13 15 17 19 21 23 25 27 29 31 33 35
50.00
-4.00
0.00
-6.00
1
-8.00
0.8
7
5.60
0.00
2
F
150.00
2.00
0.00
-2.00 1 3 5
AR(2
)
A
200.00
4.00
TS= ∑E/MAD
2.00
1.00
0.00
-1.00
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33
-2.00
-3.00
-4.00
-5.00
-6.00
-7.00
-8.00
4
7
10 13 16 19 22 25 28 31 34
A
180
160
140
120
100
80
60
40
20
0
1
3
5
7
F
9 11 13 15 17 19 21 23 25 27 29 31 33
Table 1: Performance of RNN and AR (2) model (A=Actual, F=Fitted Quarterly KZT/USD Exchange
rate1999 till 2007)
4. Conclusions
This research examined and analyzed the use of a newly developed neural network
model (RNN) in foreign exchange forecasting with KZT against USD. The RNN
model gives the evidence that there is possibility of extracting information to forecast
exchange rate reliably. The evaluation of the model is based on the estimate of mean
absolute error, R2 and tracking signal.
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