خرید و دانلود نسخه کامل کتاب Trading Systems: Theory and Immediate Practice – Original PDF

Chapter 1 Processes In finance one has to deal with a series of prices that are of a random nature. The problem of the trader – or of the investor – is to extract the signal buried in noise – if it exists – that is, to identify the stochastic process that best identifies it. In finance, we are dealing with series of prices (time series) recorded at certain instants and referred to certain assets (stocks, oil, bonds, indices, etc.). 1 Prices are normally recorded at regular intervals (15 min, 3 h, one 1 day, 1 week, etc.). If we denote by z the price of the asset under observation and by t the time at which such a price was observed, we can formally represent a time series in this way: zt; zt1; zt2; zt3; zt4 . . . It is assumed that this set of prices, to be treated for our purposes (e.g., to make predictions about future prices), follows a law of a known form. These known forms (or models or processes) are called, for example, AR, MA, ARMA, and ARIMA (we will go back to them). Such models are not deterministic. We will see in fact that a price series may be represented as in Fig. 1.1, that is, as if there was a signal (the continuous line) buried within noise, and one of our main goals will exactly be to free the signal from the noise. This means that the models we will use are very different from those described by the equations – for example – of classical mechanics, by which, given the initial position and velocity of a particle, we are able to determine exactly where the particle will be and what speed it will have at any future moment. The models that we use here are stochastic, or probabilistic, and in essence they provide us with the probability that at some future moment the price will range between two limits, one higher and one lower, according to certain criteria that we will specify.