where

Y = Market price

T = Long-term trend or secular trend C{ = Cyclical efFect

Sj = Seasonal effect Rj = Residual effect

The long-term trend, T, is a time series that describes the long-term movements of Y, or price. For example, the long-term trend of the stock market for the past 50 years has been upward for that period. This does not mean that the month-to-month or year-to-year values were always rising, but rather that there has been a long-term trend upward.

The cyclical effect, C, describes fluctuations of the value of Y about the long-term trend that can be attributed to business and economic factors. Although there has been a generally increasing long-term upward trend in stock prices, during times of recession prices fall below the long-term trend, and during general economic expansion they rise above this trend.

The seasonal efFect, S, describes the fluctuations in the time series that recur during specific portions of each year. For example, energy prices may vary during specific times of the year due to weather and growing patterns.

The residual efFect, R, is what remains after all the other components have been removed. The residual efFect results from unpredictable events, such as natural disasters, political events, and unforeseen circumstances.

It will be necessary to look to the markets in question, to determine which of these factors will be useful in the model.

Looking at the markets

The Standard & Poors 500 Index, commonly known as the S&P Index or the S&P, is a weighted index made up of the prices of 500 stocks. The S&P futures contract size is the value of the S&P Index times $500. The contract is traded at the Chicago Mercantile Exchange. The minimum fluctuation is .05, which is equal to $25.

The S&P has obvious properties, which can be seen graphically in Figure 14.1. The long-term and consistent uptrend, from the inception of this contract to 1997, is visible by even a cursory look at the chart.

On top of the long-term trend, there may be cycles, which may be political or economic in nature. For example, there may be a 4-year presidential cycle, or there may be rhythmic periods of economic financial expansion and contraction.

Treasury bonds, commonly known as the T-bonds, are long-term U.S. government debt instruments with maturities of more than 7 years. They are fixed income assets that pay interest semiannually.

The T-bond futures contract is traded at the Chicago Board of Trade. The contract size is $ 100,000, at 8 percent interest, with trading equivalent to the 30-year bond price. When interest rates rise, T-bond prices fall. This is because the existing lower interest debt instruments are less valuable. Prices are quoted as a percentage of par, and the minimum fluctuation is /32 of a point, or $31.25.

The T-bond market is well known to be strongly correlated with the S&P. Generally, the two markets move in the same direction, and confirm each other. When they move in opposite directions, it is a significant event.

It is often stated the T-bond market usually turns first-it is a leading indicator. This hypothesis is subject to interpretation, and investigation. There are a number of factors that could rationally explain such a relationship. It is well known that long-term interest rates have a powerful effect on stock market prices. Generally a bullish bond market implies rising stock prices, and vice versa. Bonds are an alternative investment for stock market investors. The public routinely moves money into the perceived safety of bonds when they have economic fears, and moves them into stocks when the economy is expanding.

Thirty-year bond yields (which are the inverse of interest rates) are influenced by inflation expectations, as opposed to short-term interest rate products, which are

Studying the Target market by Itself

The design of a specific model or indicator, or of an entire trading system, involves the concept of statistical inference. In such a design, we draw conclusions about populations based on sample observations. Samples are observed directly, and serve as approximations to the true population characteristics.

To study the market, it is often useful to transform data by using a smoothing technique to filter out random noise. For example, a simple moving average, calculated by adding up the prices of a specific number of bars, dividing that sum by the number of bars, and plotting the average on the study bar, has a smoother appearance than a line drawn through each closing price. The greater the number of bars used, the smoother the curve, as any individual price has a smaller and smaller effect on the average.

Other filtering techniques would be exponential or weighted moving averages, in which more weight is given to recent prices than remote prices. Similarly, taking the logarithm of each value or a ratio of values may help smooth the data.

In developing a model for time series data, it is often helpful to view the data graphically, and see what conclusions may be drawn from the visual pattern. With the S&P, it is clear that there has been a continuous steady long-term upward trend. However, any cyclical or seasonal patterns are not readily discernible to the eye.

For such a market, it is useful to subtract out the trend and try to determine whether there is a clear reason for the daily variation of price over time. Some of it may be cyclical or seasonal, and the rest may be random error. A first choice for a model of this data series might be as simple as a straight line, connecting the beginning and ending points, or some other simple fitting technique.

The general formula for a straight line is

YL = a+bX

affected by monetary policies of the Federal Reserve Bank. Inflation expectations reflect expectations of future monetary policy, fiscal policy, and the economy. Thus, the bond yield combines much of the core information that affects future stock prices into a single number.

Once there is an understanding of the nature of the relationship between the two data streams, it is a simple process to determine which one leads the other and by how much. This will allow us to take advantage of the relationship, by looking for divergence between the trends that describe each.

For the studies done in this chapter, we will use continuous contracts constructed from futures contract data from Genesis Financial Data Services. The continuous contracts are constructed using the roll-forward, back-adjust method, with the rollover date five trading days before the last trading day. This creates a data stream containing prices that did not actually occur, but this method maintains relative price continuity.