Single Cycle Theory

Though this classification has become popular, it is not definitely clear whether all of these cycles really exist. For example , Kondratieff was able to isolate only three long wave cycles because reliable data on industrial production only exist for the last 100- 150 years in most industrial countries , and the periodicity of the major historical innovations can be viewed as being purely accidental .
Schumpeter (1939) has already noted that superposition of different cycles may generate a rather complex overall motion. Even if single cycle would resemble harmonic wave motions, their interaction would probably not generate harmonic motions on top of longer – term harmonic waves.
It follows that it may be empirically difficult

cycles that can roughly be identified with Juglar cycles . The most interesting economic variables are therefore the national product, the aggregate price level, and unemployment rate. Some models generate harmonic time series and can be viewed as explanations for abstract and isolated Juglar or Kitchin cycles, while other models are able to generate irregular time series with varying frequencies. The common feature of most models concentrate on economic variables which exhibit an upward motion for a considerable time interval followed by a downswing and an eventual recovery ,i.e., the models concentrate on “ recurrent sequences of persistent and pervasive expansions and contractions in economic activities”. Phenomena like the structural change in a single industry , economy – wide technical progress , or adoptions to very short –term stochastic influence will be ignored in most presented models

Nevertheless, the result of more than half a century of empirical studies on financial time series indicates that this is the case if one examines their properties from a statistical point of view: the seemingly random variations of asset prices do share some quite non trivial statistical properties. Such properties, common across a wide range of instruments, markets and time periods are called stylized empirical facts.
Stylized facts are common features of the isolated empirical business cycle if the agreement on the periodic pattern and the measurement procedure has been found.
Stylized facts are thus obtained by taking a common denominator among the properties observed in studies of different markets and instruments. Obviously by doing so one gains in generality but tends to lose in precision of the statements one can make about asset returns. Indeed , stylized facts are usually formulated in terms of qualitative properties of asset returns and may not be precise enough to distinguish among different parametric models .
The observation of these dimensions is that “market activity” is strongly correlated with price