USD Exchange Rate Cycles Using Developed and Developing Currencies and Risk Factors

This paper predicts the exchange rates cyclical for US dollar [forecast two states for exchange rates; appreciation and depreciation] through using developing and developed currencies along with two risk factors (TED spreads and Inflation). Probit and logit models along with the principal component analysis and factor analysis are used to retain the most powerful components and factors. The empirical findings reveal that risk factors are not key factors in determining the exchange rates' cyclical behavior for the US dollar. Furthermore, the Sterling Pound is the only variable that has a consistent result that is more likely to cause appreciation for the US dollar exchange rate using all types of regressions. In addition, Renminbi shows inconsistent effects between different regressions; using OLS is less likely to cause appreciation for the US dollar exchange rate. By contrast, using Logit and Probity regressions is more likely to cause appreciation for the US dollar exchange rate. On the other hand, principal component analysis and factor analysis show that for all currencies we should retain two components and factors to be able to explain around 80% of the variation in exchange rate cyclical.


INTRODUCTION
Jameel and Stefan (2015) define the exchange rate as "the relative price of one currency in terms of another". In addition, this tool can be considered an essential macroeconomic indicator for competitive power for countries. (Cheung, Chinn, Pascual, & Zhang, 2019) compare the random walk benchmark performance with the performance of a bunch of models in predicting the exchange rates and conclude that co-integrated exists between predicted values and actual exchange rates value, and the elasticity of forecasted values is different than one. This paper investigates using several developing and developed currencies besides two risk factors (TED spreads and the inflation) in predicting the exchange rates cyclical behavior for US dollar [appreciation (bull), depreciation (bear)] using dynamic probit and logit models. In addition, I use the principal component analysis and factor analysis to know the components and factors that I should retain. The findings affirm that risk factors are not key factors in determining the exchange rates cyclical behavior for US dollar. Moreover, Sterling pound is the only currency that has a consistent result and is more likely to cause appreciation for US dollar exchange rate at all types of regressions. Furthermore, Renminbi shows inconsistent effects. In addition, On the other hand, principal component analysis and factor analysis show that for all currencies we should retain two components and factors to be able to explain around 80% of the variation in the data.
This study contributes to the existing finance literature, where this paper is the first paper that uses the principal component analysis and factor analysis techniques to predict the exchange rates cyclical. Also, the sample of this paper uses vast number of currencies; includes both developed and developing currencies, while the past literature concentrates only on the developed countries. examine the role of exchange rates movements in impacting the inflation rate in UK. (Byrne, Korobilis, & Ribeiro, 2018) test the source of uncertainty in exchange rate forecasting models such as random variations in the data and estimation uncertainty, they find that those furcating model present more accurate results than the drift less random walk benchmark at all horizons. Moreover, using the benchmark allows to identify the set of related explanatory variables and the tine-varying weights for those explanatory variables. (Chen, Zeng, & Lee, 2018) find consistent mild RMB undervaluation as well as overvaluation across time, all Asian countries in their study have affected by RMB misalignments. (Baghestani & Toledo, 2017) show that there is a directional predictability for the US-Australia (US-UK) exchange rate between (1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007) but that does not work for the period (2008-2015) that makes difference between analysts' and random walk forecasts between them. On the other hand, (Tsuchiya & Suehara, 2015) show that for the short-term the exchange direction is not predictable as the long-term where the government keeps its foreign exchange policy over time (Beckmann, Belke, & Kühl, 2011).

H1:
The two risk factors with all currencies can predict the exchange rates cyclical behavior for US dollar to be bull (appreciation).
H2: The two risk factors with all currencies can predict the exchange rates cyclical behavior for US dollar to be bear (depreciation).
H3: We will retain all components from our PCA analysis.
H4: We will retain all factors from our factor analysis.

United Frontiers Publisher
Journal of Advances in Humanities Research 45

METHODOLOGY, SAMPLE AND DATA
In this study, I examine the predictability of exchange rate cycles for ten exchange rate, Japanese yen (JPY), Indian rupee (

THE MODEL
I use asset price view of the exchange rate, and this currency price shows cyclical patterns, these series of patterns are basically binary events. So that, our model will start with binary modeling framework (binary event), with underlying unobserved process as follows: Where is the underlying unobserved process?
: is the risk factors vector as cross-country differences (home minus foreign).
Because is unobserved we will follow cycles via Bry and Boschan (1971)'s nonparametric to create the binary variable as follows: (2) Setting as i.i.d in the probit model we will have the followings: Where represents the exchange rate cycles.

Journal of Advances in Humanities Research 46
To account for persistence of asset price cycles we add the lagged dummy as exogenous variable, so the dynamic model will be as follows:

) (4)
Following the literature as Kauppi and Saikkonen (2008) the lag h should match the forecast horizon. All parameters ( , are estimating using the means of the method of the likelihood. After that we will estimate in-sample as Estrella (1998) using Pseudo-It compares the unconstrained and the constrained models based on the likelihood values, its formula will be as follows:

Pseudo-(5)
To estimate we restrict model (4) by assuming = as Kauppi and Saikkonen, (2008). However, as (Dueker, 1997) we should start with zero pseudo-R2 value by assuming in equation (4)in order to assess the explanatory power and the relevance of the included variable , the resulting statistic can be seen as an incremental pseudo-R2. On the other hand, for out-of-sample forecasts. We will use again Kauppi and Saikkonen (2008) and use iterated forecasting procedures. Specifically, h periods ahead forecasts can be calculated iteratively as follows: Where are the probabilities of to be either zero or one, conditional on information known in the forecast period . In addition, to evaluate the out-of-sample forecasts. I assigned the value 1 for appreciation in the US dollar (bull), and the value 0 for depreciation in the US dollar (bear) for the logit and probit models.

Variables Definitions:
US: is the dependent variable and it is a binary variable takes the value 1 for appreciation in the US dollar, and the value 0 for depreciation in the US dollar.          We can observe in table 10 that we again retain just two factors, because they have the best explanation power for variation in data. In addition, the last column is the uniqueness of these factors versus the commonality in explaining variation, the uniqueness is reversely related to commonality which can be calculated as commonality = 1-uniqueness value.
Uniqueness is the error term of variable that is not explained by the variable and the commonality is the opposite which is explained by the variable.