Two of the simplest and most widely used technical rules are investigated: Moving- Average Oscillator and Auto-Regressive Models. Moving averages have been the subject of more discussion in most technical analysis than any other technical indicators and are widely used by financial trading institutions. At a later stage of the paper, the use of basic trading tools such as Support and Resistance lines to indicate key reversal areas is examined. In its simplest form, the moving average is a very traditional way of smoothing cyclical fluctuations. The basic analysis consists of two parts:

· the data in the time series is smoothed by calculating an arithmetic moving average series of the data

· each number from the original series is divided by an average from the moving average series.

In this exercise, popular short and long-period, 5 (five), 10 (ten), 15 (fifteen) and 50 (fifty) week moving-averages are utilised. Buying and selling signals are generated when the short period moving average rises above (or falls below), the long period moving averages. When the short-period moving average penetrates the long-period moving averages, a trend is considered to exist, and theoretically traders can generate profits from trading the market.

The moving average rules are often modified by the introduction of a band around the moving averages. The objective of the band, which in this case is the funding cost, is to reduce the number of buy (sell) signals by eliminating weak signals when the short and long-period moving averages are very close. Buying and selling signals are generated only when the differences between prices and moving averages (for single moving average) or between long and short moving averages (in the case of two-period moving averages) are greater than the foreign exchange and interest rate spreads.

Mathematically the trading rules in their simplest form can be expressed as follows:

Rule 1: If (PMA(n period) < Pt) then "Sell"

Rule 2: If (PMA(n period) > Pt) then "Buy"

where PMA(n period): the moving average price of n period, and

Pt : the current price.

When including the funding costs as bands then the trading rules can be modified to:

Rule 1: If PMA(n period) - Pt >Funding Costs then "Sell"

Rule 2: If Pt - PMA(n period) > Funding Costs then "Buy"

where PMA(n period): the moving average price of n period, and

Pt : the current price.

The rules were extended so that the signals were generated only if the differences cover the costs of funding, in this case the Foreign Exchange and Interest Rate Spreads. Foreign Exchange spread in this research is 14 (seven) basis point or 0.0014 for each buying (selling) and reselling (re-buying) on the basis of Australian Dollar which represents foreign exchange transaction cost, while the interest rate spread is 2 basis point or 0.02% which represent the money market transaction costs.

Profit or Loss of the trading is computed as realisation of the foreign exchange prices differences and the interest cost/gain (or referred to as Net Funding Cost) associated with buying/selling the currencies. The formula used for profit/loss computation in terms of Australian Dollar is as follows [Tan, 1997]:

where:

Io: Initial Outlay, or the Amount of Investment in terms of Local Currency, in this case Australian Dollars
fx: Foreign Exchange Rates
fxspr: Foreign Exchange Rate bid/ask spread
ilocal: Local Interest Rate
iforeign: Foreign Interest Rate
ispr: Interest Rate bid/ask spread

Additional filter rules are introduced to eliminate whipsaws or unnecessary trading signals. In this paper, initial experiments are performed without any filter, with subsequent filters of 0.5, 1.0 and 1.5 percent being used. The filter eliminates any signals where the differences between current week and previous week are less than the filter values. The initial test is to examine the statistical properties of the Australian Dollar data time series. It is important to see if any unusual pattern existed from time to time, or in other words, do trends in Australian Dollar market change from time to time. Since the period used for the test is from 1st January 1986 to 23rd June 1999, then the whole series are arbitrarily divided into 3 (three) different sub-periods as follows:

· First sub-period, weekly time series, which starts from 1st January 1986 to 20th June 1990.

· Second sub-period, weekly time series, which starts from 27th June 1990 to 14th December 1994.

· Third sub-period, weekly time series which starts from 21st December 1994 to 23rd June 1999.

Table 1 contains summary statistic results and the auto-correlation coefficients for the entire series and three sub-samples prices of the Australian Dollar market over the tested period.

Table 1: Statistic Summary Results are presented for the full sample and 3 non-overlapping sub-periods as relative comparison. r(i) is the estimated auto-correlation at lag i for each series.

The results showed that volatility was the highest during the third sub-period which started from 21st December 1994 to 23rd June 1999, measured in terms of ’Sample Variance’ or ’Standard Deviation’, as seen in Chart 1. It was contributed from the fact that Australian Dollar had been depreciating against US Dollars during the third sub-period. The triggering event that reversed the up-trend was Australia’s biggest share market loss of $13 billion in a single day as the weight of the Asian slumps hit world markets on 27th October 1997.

Later on 8th June, 1998, international speculators sold Australian Dollars below 60 US cents (more than A$ 1.67 per US $1), a level not seen since July 1986 [Colebatch, 1998]. Other than that, the table shows that generally there should not be any material difference in time series among the sub-periods, which means that it is possible to build a profitable trading system for the entire period. The research methods of the paper are performed in three stages:

· Comparison of Single and Two Moving Averages, and ARMA Model – with and without filter rules – using in-sample and out-of-sample data.

· Single and Two Moving Averages – with and without filters.

· Single Moving Averages using Support and Resistance as Filter Rules

Prof. Clarence N W Tan and Herlina Dihardjo

Next: Single and Two Moving Averages - In and out-of-sample data

Summary: Index