{"id":1287,"date":"2026-01-26T18:38:47","date_gmt":"2026-01-26T08:38:47","guid":{"rendered":"https:\/\/archive4ones.com\/2ndstudy\/?p=1287"},"modified":"2026-01-27T12:21:19","modified_gmt":"2026-01-27T02:21:19","slug":"year11-math-1-2-22-time-series-analysis","status":"publish","type":"post","link":"https:\/\/archive4ones.com\/2ndstudy\/?p=1287","title":{"rendered":"Year11-MATH-2-4-5 Time Series Analysis"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">In the QCAA <strong>General Mathematics<\/strong> syllabus for Year 12, <strong>Unit 3<\/strong> includes several core topics that cover data analysis, financial modeling, and geometry.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Time Series Analysis<\/strong>&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">Time series analysis involves studying data points indexed in chronological order to identify patterns and forecast future values. Key components include:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Time Series Plots:<\/strong> Graphs where time is the explanatory variable on the horizontal axis and a response variable is on the vertical axis.<\/li>\n\n\n\n<li><strong>Identifying Patterns:<\/strong> Recognizing secular trends (long-term direction), seasonal variations (regular intervals), cycles, and random fluctuations.<\/li>\n\n\n\n<li><strong>Smoothing:<\/strong> Using <strong>moving means<\/strong> (moving averages) to reduce &#8220;noise&#8221; and better see underlying trends.<\/li>\n\n\n\n<li><strong>Deseasonalising:<\/strong> Adjusting data using <strong>seasonal indices<\/strong> to account for regular seasonal peaks or troughs.<\/li>\n\n\n\n<li><strong>Forecasting:<\/strong> Using a fitted trend line (often a least-squares regression line) to predict future values.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Sequences (Arithmetic and Geometric)<\/strong>&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">These are covered under the &#8220;Growth and Decay in Sequences&#8221; topic and are used for recursive modeling:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Arithmetic Sequences:<\/strong> Characterized by a constant common difference (<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>d<\/mi><annotation encoding=\"text\/plain\">d<\/annotation><\/semantics><\/math>). They model linear growth\/decay, such as simple interest or straight-line depreciation.<\/li>\n\n\n\n<li><strong>Geometric Sequences:<\/strong> Characterized by a constant common ratio (<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>r<\/mi><annotation encoding=\"text\/plain\">r<\/annotation><\/semantics><\/math>). They model exponential growth\/decay, such as compound interest, reducing balance depreciation, or population growth.\u00a0<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Earth Geometry<\/strong>&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">This topic focuses on positioning and distance on the Earth&#8217;s surface:&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Positioning:<\/strong> Using latitude (parallels) and longitude (meridians) to locate points.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Distances:<\/strong> Calculating arc lengths along great circles and small circles using angle measurements.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Time Zones:<\/strong> Calculating time differences between locations based on their longitudinal distance from the Prime Meridian.&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p 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Series Analysis&nbsp; Time series analysis involves studying data points indexed in chronological order to identify patterns and forecast future values. Key components include:&nbsp; Sequences (Arithmetic and Geometric)&nbsp; These are covered under [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-1287","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1287","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1287"}],"version-history":[{"count":3,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1287\/revisions"}],"predecessor-version":[{"id":1369,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1287\/revisions\/1369"}],"wp:attachment":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1287"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1287"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}