I am looking for a mathematical operation that can help me express daily data as weekly and monthly. I mean that I have $100$ daily observations and I am trying to produce an equation of the form $$ V=C+x_{1}V_{d}+x_{2}V_{w}+x_{3}V_{m}, $$ where $C$ is a constant, $x_{i}$ are coefficients and
$$ \begin{align*} V_{d} & = \,\, \text{daily realised volatility} \\ V_{w} & = \,\, \text{weekly realised volatility} \\ V_{m} & = \,\, \text{monthly realised volatility} \\ \end{align*}$$ However, my statistical package (EViews) allows me to enter only series of the same frequency, hence, I can't do it in the normal way. This means that I have to use the daily observations for all three terms. Does anyone know a way of changing daily data to weekly and monthly?
To convert realised variance from a weekly rate to a daily rate, we divide by $5.$ To convert realised variance from a monthly rate to a daily rate, we divide by $22.$ Volatility is just the square root of the variance. So we get $$ \begin{align*} V_{w} & \rightarrow \frac{V_{w}}{\sqrt{5}} \\ V_{m} & \rightarrow \frac{V_{m}}{\sqrt{22}} \end{align*} $$ so that your equation should become $$ V = C + x_{1}V_{d} + x_{2}\frac{V_{w}}{\sqrt{5}} + x_{3}\frac{V_{m}}{\sqrt{22}} $$ The volatilities should now all be at a daily rate.