Diversified mining stocks may come under further selling pressure in the short-term, but the long-term story looks positive, according to broker Canaccord Genuity. Analysts recommended investors "build positions in this period of share-price weakness".After recent dramatic falls in metal prices - in some cases to five-year lows - downgrades to commodity-price forecasts may limit gains across the mining sector, the broker said, given that valuations have not yet fully reflected these adjustments."While mining share prices have pulled back, we think there may be more downside in the coming weeks," it added.Furthermore, Canaccord reckons that if price declines are prolonged then it will "seriously limit the ability of the diversified miners to commit to major increases in shareholder returns without re-gearing their balance sheets".Nevertheless, taking a long-term view the broker said that recent concerns about a slowdown in global economic growth, particularly in China, are "overdone"."We believe that at current commodity prices there is more upside potential than downside risk in both commodity prices and for the large diversified mining equities," Canaccord said."The majors are well positioned on the cost curve and are still in a position to consider increasing shareholder returns; it is generally the smaller single commodity plays that are struggling."Canaccord has initiated coverage of Glencore and Anglo American with 'buy' ratings and started with a 'hold' at Vedanta. Rio Tinto is still rated a 'buy', while BHP Billiton was maintained at 'hold'.The broker said that Rio remains its top pick and "looks cheap on most metrics".