A condition of mispricing between two markets that offers an opportunity for riskless profits and is expected to disappear rapidly. An example arbitrage: suppose gold is selling in Chicago for $300 an ounce and in New York for $320 an ounce. Suppose also that it only costs $1 an ounce to ship gold from Chicago to New York. One could buy gold in Chicago and sell gold short in New York simultaneously, for a riskless arbitrage profit of $19 an ounce. Arbitrage opportunities like this are rare and last only briefly most of the time. In fact, the absence of arbitrage opportunities is the foundation of modern finance theory; see [Elton Gruber 1984].
A statistical procedure that computes the correlation coefficients for a set of input variables. Each pair of variables has a correlation coefficient. The output of a correlation analysis is usually a correlation matrix, a table of the coefficients in a square array.
A statistical measure of the direction and magnitude that one variable moves when a second variable moves upwards. If variable A moves up when variable B moves up, A and B are positively correlated and the coefficient will be positive. If variable A moves down when variable B moves up, A and B are negatively correlated and the coefficient will be negative. If A moves up and B doesn't move at all, the variables are uncorrelated (independent) and the coefficient is zero.
A trading strategy that attempts to profit from short-term moves in reaction against the major trend of a market. Most counter-trend strategies use oscillators or momentum indicators to locate times when a market is overbought in an uptrend or oversold in a downtrend, then taking a position counter to the trend.
A component of a time series that oscillates up and down over the course of a number of months or years, usually with a period of greater than a year. The most common cyclic component in economic time series is the so-called business cycle.
Remove the seasonal component from a time series, leaving the trend, cyclic and irregular components.
Remove the trend component from a time series, leaving the seasonal, cyclic and irregular components.
A statistically derived artificial variable that is a linear combination of the original given variables. Factors are computed by either principal component analysis or factor analysis.
A statistical procedure for reducing the dimensionality of a data set by approximating the given variables as linear combinations of factors than are uncorrelated with each other. Factor analysis is very similar to principal component analysis and can also be found in most statistical packages. In fact, the underlying computations are often identical and the major difference is in how the results are presented and interpreted. In principal component analysis, the emphasis is on the reduction of dimensionality and the factors are almost always uncorrelated with each other. In factor analysis, the emphasis is on understanding what the factors mean in terms of the original problem, and factors may be rotated and may actually be correlated with each other if that leads to a greater understanding of the problem. See [Rayment Joreskog 1996] for more details.
The correlation coefficients between the original input variables and the factors derived by a factor analysis.
The component that remains after the trend, cyclic and seasonal components have been removed from a time series.
The total gain or loss from a stock over a month, expressed as a percentage change, including both price changes and dividend payments. Example: suppose you bought 100 shares of Consolidated Factor Loadings (CFL) on the first trading day of January at $100 a share. In January, CFL paid a dividend of 10 cents a share and on the first trading day of February, the price of CFL is $110. Your $10,000 investment is now worth $11,010, including the dividend. The monthly return is 11010/10000 1, or 10.1%
Principal Component Analysis
A statistical procedure for reducing the dimensionality of a data set by approximating the given variables as linear combinations of factors than are uncorrelated with each other. A large number of input variables will usually yield a much smaller set of factors. Most statistical packages provide principal components analysis.
The component of a time series that varies with the calendar seasons. That is, it is a repetitive component with a period of one year.
An index which shows the seasonal component of a time series independent of its other components.
Opposing market positions entered simultaneously in two or more markets or contracts. Example spreads: A long futures contract in July Corn and a short futures contract in December Corn. This is a calendar spread. The trader would profit if the price difference, July minus December, increased and would lose if it decreased. A long futures contract in December Corn and a short futures contract in December Soybeans. This is an intercrop spread. The trader would profit if corn prices rose relative to soybeans and lose if corn prices dropped relative to soybeans. A long position in soybeans and a short position in soybean meal and soybean oil. This is called a "crush spread".
Spread traders, like arbitrage traders, attempt to profit from relative mispricings in markets, but the mispricings are less clearly defined than they are in an arbitrage, and usually last longer before coming to a balance. Spreads are often believed to be less risky than outright long or short positions, but they are also less profitable.
A collection of data points indexed by time. CSI financial market data are indexed by trading day, but other economic time series are often indexed by week, month, quarter or year.
Time Series Decomposition
The process of decomposing a time series into components. In classical time series analysis, a time series is represented as the sum or product of four components: trend, seasonal, cyclic and irregular. Decomposition is the process of determining the components from a time series.
In time series analysis, a trend is a long-term movement in a single direction, up or down. A trend may be linear a straight line or curvilinear a curve. In technical analysis of markets, a trend may exist on any time scale. So the two usages of the term are similar but not exactly the same.
A trading strategy that attempts to profit from major long-term moves in a market. Trend-following systems typically use indicators like moving averages or channel breakouts to locate when a major up move or down move is occurring. The basic principle is, as the name implies, following the market. A trend-following system usually enters after a trend has established itself, thus missing the initial turning point. A trend-following system may exit on small turns opposite the trend and re-enter should the trend resume, or it may wait until the turn has established itself as a trend in the opposite direction before exiting.