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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?

Docksan
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  • I think it would help if you defined the terms in your equation.

    Also, see here to help you express it more clearly (it is not clear if some letters you have used are subscripts or factors in a product, for example): http://math.stackexchange.com/help/notation

     – Shai Dec 30 '14 at 21:58
  • If I understand you correctly, you want to know what RVd, RVw and RVm are? These are daily realized volatility-RVd (a single from my observations), weekly realized volatility RVw (the sum of 5 RVd divided by 5) and monthly realized volatility RVm (the sum of 22 RVd divided by 22). The x are just coefficients, and C is a constant. – Docksan Dec 30 '14 at 22:05

1 Answers1

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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.

Shai
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