Key to understanding Faulkner's framing of the story with the old chivalric code of the ghostly Old South's past with Part I and Part V, is his creation of a gothic horror with the gruesome details of a past perverted by noblesse oblige and the lost moments of youth tainted with age and grotesquely reclaimed in the present. Indeed, Faulkner has arranged his narrative in the order of one of his statements:

Thus she passed from generation to generation--dear, inescapable, impervious, tranquil, and perverse.

 

Although time is present in "A Rose for Emily," the story unfolds not in linear fashion--beginning, middle, and end--but in a series of episodes that can be approximately dated (see, for example,  Paul McGlynn's essay "The Chronology of 'A Rose for Emily'").   It's often useful to do a rough chronology of the story just to understand the number of decades that encompassed Miss Emily's life, but I would suggest that Faulkner chose his non-linear narrative technique in order to mirror Miss Emily's own perception of life, which does not seem to have included an understanding or acknowledgement of time's passing.

From the beginning of the story to its end, we are confronted with Miss Emily's resolute refusal to acknowledge time--she refuses to pay taxes and sends the town officials to a long-dead Colonel Sartoris for an explanation; she disappears from public view for years at a time, residing within a house that ages only in a physical sense; she sleeps with a man who has been dead for about thirty years in a room decorated for a marriage celebration.  

Miss Emily's life, from the time of young womanhood, has been spent "out of time"--in a vacuum created in her mind and completely unaffected by the passage of time in the world outside.   Faulkner recounted her life in episodes because that is how she experienced life, not as a sequence of events, but as a series of events that were separate from the life of the town and time as most of us perceive it.

Putting the story's "ending" at the beginning is a method of creating tension and suspense in fiction. This method is often used in film as well. 

When the audience has a specific event, episode, or idea to anticipate, the story becomes naturally imbued with some amount of tension. The question of the story presents to the reader becomes a "how" question (How does the predicted outcome come to pass?), which is a twist on the more-or-less standard "what" question in narrative (What happens in the story?). 

Faulkner uses this method well and subtly undermines the certainty with which he begins the story. At the opening, a simple and definite event is predicted. By the end, that same event is no longer so simple or definite because we have come to learn so much about the character.

One of the things that makes "A Rose for Emily" such a classic short story is Faulkner's use if a fractured time line.  The story is written in parts; each part gives certain details about the mysterious Miss Emily Grierson.  

Faulkner was having fun with the reader.  He knew it would a little frustrating to not have the story written in an ordinary order.  If the story were told in chronological order, the story would not be in the realm of a masterpiece in American literature. 

If the reader begins at the start of the story, it is the funeral of Emily.  The story ends after her funeral with the citizens coming into her house to find out about what has been up in the upstairs bedroom.  Now what happens in between has to be put in order. 

Chronologically, in the first section, you are given a date 1894 when Colonel Sartoris paid Emily's taxes. 

In section two, the smell that came from Emily's house was thirty years before the new councilmen came to get Emily to pay her taxes.  This was two years after her father's death. It was also a short time after Homer Barron disappeared.  

She was about 30 when her father died.  

In section three, about a year later after her father died, Homer Barron comes to town. Emily would have been about 31 years old. 

This is the time that she went riding with Homer.  Her cousins came. She bought arsenic and the men's clothing. 

Section four

Shortly, after this, Homer disappeared after being seen going in the backdoor of Emily's house.We learn that Emily was 74 years old when she died. 

From this point, the reader should be able to see how to put the entire story in chronological order.   It should be easy because there are not that many new events in the last section other than finding Homer's skeleton in bed with Emily's gray hair on the pillow next to him. 

What a fun story!

One of the reasons that the story is not told in order is that the plot is not as important as the theme.  Like the characters, we are left to experience the story in pieces until we get the whole thing, and realize what Emily's story has to tell us about love, pride, and tradition.