The increasing order of the reactivity of the following halides towards ${\mathrm{SN}}^1$ reaction is 

 

Order of reactivity for ${\mathrm{SN}}^1$ reaction is in accordance to the order of stability of carbocation involved

I produce $2^0 carbocation$

II produce $1^0 carbocation$

III produce P- methoxy benzylic cation 

The order of stability of carbocations formed is $1^0< 2^0<P- methoxy benzylic cation$ 

Therefore  the order of stability is   II < I < III