Let f"tg be a stationary process and xt = a + b t + "t with a and b constants. (a) Show that rxt is stationary. (b) How would you obtain a stationary process stationary if the trend were quadratic? ...

Let f"tg be a stationary process and xt = a + b t + "t with a and b

constants.

(a) Show that rxt is stationary.

(b) How would you obtain a stationary process stationary if the trend

were quadratic?

Let f_tg be a sequence of independent random variables normally distributed,

zero-mean and variance _2. Let a, b and c be constants Which of

the following processes are stationary? For each statiuonary process calculate

its expected value and its autocovariance function.

(a) xt = a + b _t + c_t􀀀1,

(b) xt = a + b _0,

(c) xt = _1 cos(ct) + _2 sin(ct),

(d) xt = _0 cos(ct),

(e) xt = _t cos(ct) + _t􀀀1 sin(ct),

(f) xt = _t_t􀀀1.