BUS606: Operations and Supply Chain Management

The business cycle is a quasi-periodic oscillation characterized by periods of expansion and contraction of the economy, lasting on average from three to five years. Because most time series are too short for the identification of a trend, the cycle and the trend are estimated jointly and referred to as the trend-cycle. As a result the concept of trend loses importance. The trend-cycle is considered a fundamental component, reflecting the underlying socio-economic conditions, as opposed to seasonal, trading-day and transient irregular fluctuations.

The proper identification of cycles in the economy requires a definition of contraction and expansion. The definition used in capitalistic countries to produce the chronology of cycles is based on fluctuations found in the aggregate economic activity. A cycle consists of an expansion phase simultaneously present in many economic activities, followed by a recession phase and by a recovery which develops into the next expansion phase. This sequence is recurrent but not strictly periodic. Business cycles vary in intensity and duration. In Canada for example, the 1981 recession was very acute but of short duration, whereas the 1991 recession was mild and of long duration. Business cycles can be as short as 18 months and as long as 10 years.

A turning point is called a peak or downturn when the next estimate of the trend-cycle indicates a decline in the level of activity; and a trough in the opposite situation. There are many ways to determine when a downturn occurs, but in general, a downturn is deemed to occur at time t in the trend-cycle of monthly series, if

$c_{t-l} \leq \ldots \leq_{c_{t-1}}>c_{t} \geq c_{t+1}$                                                         (12.a)

and an upturn, if

$c_{t-l} \geq \ldots \geq c_{t-1} \text { < } c_{t} \leq c_{t+1}$.                                                    (12.b)

Thus, a single change to a lower level $c_{t}$ , between $t+1$ and $t$, qualifies as a downturn, if $c_{t+1} \leq c_{t}$ and $c_{t-3} \leq c_{t-2} \leq c_{t-1}$; and conversely for an upturn.

The dating of downturns and upturns is based on a set of economic variables related to production, employment, income, trade and so on.

Similarly to the trend, the models for cyclical variations can be deterministic or stochastic. Deterministic models often consist of sine and cosine functions of different amplitude and periodicities. Stochastic models of the ARIMA type, involving autoregressive models of order 2 with complex roots, have been used to model business cycles.