{"id":24846,"date":"2025-03-04T15:57:30","date_gmt":"2025-03-04T14:57:30","guid":{"rendered":"https:\/\/qooant.com\/?p=24846"},"modified":"2025-03-07T13:19:50","modified_gmt":"2025-03-07T12:19:50","slug":"lognormal","status":"publish","type":"post","link":"https:\/\/qooant.com\/ca\/lognormal\/","title":{"rendered":"Distribuci\u00f3 normal i lognormal"},"content":{"rendered":"

Per a explicar aquest apartat partirem d\u2019un cas pr\u00e0ctic: Agafem com a exemple el moviment de l\u2019EURUSD i triem com a per\u00edode de c\u00e0lcul el d\u2019una hora.<\/span><\/p>\n

Hem de tenir en compte que podriem haver agafat qualsevol per\u00edode per a fer l\u2019exemple (un minut, 5 minuts, una setmana, etc.).<\/span><\/p>\n

Agafem com a preu la mitjana entre el preu ask i el preu bid.<\/span><\/p>\n

Calculem la variaci\u00f3 hor\u00e0ria del moviment de l\u2019EURUSD d\u2019un dia qualsevol.<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
<\/td>\n<\/td>\n<\/td>\n<\/td>\nVariaci\u00f3 hor\u00e0ria<\/b><\/td>\n<\/tr>\n
Hora<\/b><\/td>\nAsk<\/b><\/td>\nBid<\/b><\/td>\nPreu<\/b><\/td>\nEn preu<\/b><\/td>\nEn Pips<\/b><\/td>\n<\/tr>\n
1:00:00<\/span><\/td>\n1,08117<\/span><\/td>\n1,08115<\/span><\/td>\n1,08116<\/span><\/td>\n0,00000<\/span><\/td>\n0<\/span><\/td>\n<\/tr>\n
2:00:00<\/span><\/td>\n1,08215<\/span><\/td>\n1,08212<\/span><\/td>\n1,08214<\/span><\/td>\n0,00097<\/span><\/td>\n97,5<\/span><\/td>\n<\/tr>\n
3:00:00<\/span><\/td>\n1,08187<\/span><\/td>\n1,08184<\/span><\/td>\n1,08186<\/span><\/td>\n-0,00028<\/span><\/td>\n-28<\/span><\/td>\n<\/tr>\n
4:00:00<\/span><\/td>\n1,08171<\/span><\/td>\n1,08170<\/span><\/td>\n1,08171<\/span><\/td>\n-0,00015<\/span><\/td>\n-15<\/span><\/td>\n<\/tr>\n
5:00:00<\/span><\/td>\n1,08140<\/span><\/td>\n1,08137<\/span><\/td>\n1,08139<\/span><\/td>\n-0,00032<\/span><\/td>\n-32<\/span><\/td>\n<\/tr>\n
6:00:00<\/span><\/td>\n1,08124<\/span><\/td>\n1,08122<\/span><\/td>\n1,08123<\/span><\/td>\n-0,00015<\/span><\/td>\n-15,5<\/span><\/td>\n<\/tr>\n
7:00:00<\/span><\/td>\n1,08091<\/span><\/td>\n1,08091<\/span><\/td>\n1,08091<\/span><\/td>\n-0,00032<\/span><\/td>\n-32<\/span><\/td>\n<\/tr>\n
8:00:00<\/span><\/td>\n1,08127<\/span><\/td>\n1,08126<\/span><\/td>\n1,08127<\/span><\/td>\n0,00036<\/span><\/td>\n35,5<\/span><\/td>\n<\/tr>\n
9:00:00<\/span><\/td>\n1,08112<\/span><\/td>\n1,08110<\/span><\/td>\n1,08111<\/span><\/td>\n-0,00016<\/span><\/td>\n-15,5<\/span><\/td>\n<\/tr>\n
10:00:00<\/span><\/td>\n1,08162<\/span><\/td>\n1,08156<\/span><\/td>\n1,08159<\/span><\/td>\n0,00048<\/span><\/td>\n48<\/span><\/td>\n<\/tr>\n
11:00:00<\/span><\/td>\n1,08108<\/span><\/td>\n1,08105<\/span><\/td>\n1,08107<\/span><\/td>\n-0,00052<\/span><\/td>\n-52,5<\/span><\/td>\n<\/tr>\n
12:00:00<\/span><\/td>\n1,08189<\/span><\/td>\n1,08187<\/span><\/td>\n1,08188<\/span><\/td>\n0,00081<\/span><\/td>\n81,5<\/span><\/td>\n<\/tr>\n
13:00:00<\/span><\/td>\n1,08132<\/span><\/td>\n1,08129<\/span><\/td>\n1,08131<\/span><\/td>\n-0,00057<\/span><\/td>\n-57,5<\/span><\/td>\n<\/tr>\n
14:00:00<\/span><\/td>\n1,08129<\/span><\/td>\n1,08127<\/span><\/td>\n1,08128<\/span><\/td>\n-0,00002<\/span><\/td>\n-2,5<\/span><\/td>\n<\/tr>\n
15:00:00<\/span><\/td>\n1,08221<\/span><\/td>\n1,08199<\/span><\/td>\n1,08210<\/span><\/td>\n0,00082<\/span><\/td>\n82<\/span><\/td>\n<\/tr>\n
16:00:00<\/span><\/td>\n1,08356<\/span><\/td>\n1,08354<\/span><\/td>\n1,08355<\/span><\/td>\n0,00145<\/span><\/td>\n145<\/span><\/td>\n<\/tr>\n
17:00:00<\/span><\/td>\n1,08308<\/span><\/td>\n1,08306<\/span><\/td>\n1,08307<\/span><\/td>\n-0,00048<\/span><\/td>\n-48<\/span><\/td>\n<\/tr>\n
18:00:00<\/span><\/td>\n1,08379<\/span><\/td>\n1,08376<\/span><\/td>\n1,08378<\/span><\/td>\n0,00071<\/span><\/td>\n70,5<\/span><\/td>\n<\/tr>\n
19:00:00<\/span><\/td>\n1,08408<\/span><\/td>\n1,08406<\/span><\/td>\n1,08407<\/span><\/td>\n0,00029<\/span><\/td>\n29,5<\/span><\/td>\n<\/tr>\n
20:00:00<\/span><\/td>\n1,08415<\/span><\/td>\n1,08412<\/span><\/td>\n1,08414<\/span><\/td>\n0,00006<\/span><\/td>\n6,5<\/span><\/td>\n<\/tr>\n
21:00:00<\/span><\/td>\n1,08374<\/span><\/td>\n1,08373<\/span><\/td>\n1,08374<\/span><\/td>\n-0,00040<\/span><\/td>\n-40<\/span><\/td>\n<\/tr>\n
22:00:00<\/span><\/td>\n1,08408<\/span><\/td>\n1,08372<\/span><\/td>\n1,08390<\/span><\/td>\n0,00016<\/span><\/td>\n16,5<\/span><\/td>\n<\/tr>\n
23:00:00<\/span><\/td>\n1,08407<\/span><\/td>\n1,08395<\/span><\/td>\n1,08401<\/span><\/td>\n0,00011<\/span><\/td>\n11<\/span><\/td>\n<\/tr>\n
0:00:00<\/span><\/td>\n1,08421<\/span><\/td>\n1,08421<\/span><\/td>\n1,08421<\/span><\/td>\n0,00020<\/span><\/td>\n20<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

La distribuci\u00f3 estad\u00edstica que m\u00e9s s\u2019apropa al moviment de la variaci\u00f3 de preus \u00e9s la <\/span>distribuci\u00f3 normal<\/b>.\u00a0<\/span><\/p>\n

La distribuci\u00f3 normal t\u00e9 una s\u00e8rie de caracter\u00edstiques que s\u2019aprofiten per al c\u00e0lcul quantitatiu d\u2019actius financers donada la seva aproximaci\u00f3 al moviment real d\u2019aquests.<\/span><\/p>\n

El cas m\u00e9s clar \u00e9s la volatilitat.<\/span><\/p>\n

La volatilitat va associada al concepte de desviaci\u00f3 est\u00e0ndard d\u2019una distribuci\u00f3 normal.<\/span><\/p>\n

Nota<\/i><\/b>. Aplicarem la f\u00f3rmula de la \u201cDesviaci\u00f3 Est\u00e0ndard Mostral\u201d que canvia lleugerament respecte a la de la \u201cDesviaci\u00f3 Est\u00e0ndard Poblacional\u201d.<\/span><\/i><\/p>\n

\"\"<\/p>\n

s <\/b>\u00b7 Desviaci\u00f3 est\u00e0ndard mostral.<\/span><\/p>\n

n <\/b>\u00b7 Grand\u00e0ria de la mostra.<\/span><\/p>\n

x<\/span>i<\/span> \u00b7 Observacions de la mostra.<\/span><\/p>\n

x\u0304 \u00b7 Mitjana de la mostra.<\/span><\/p>\n

Per exemple, tenint en compte la mostra hor\u00e0ria de variacions de preu anterior (en pips) tenim els seg\u00fcents resultats:<\/span><\/p>\n\n\n\n\n\n
n<\/span><\/td>\n 24\u00a0<\/span><\/td>\n<\/tr>\n
x\u0304<\/span><\/td>\n 12,71\u00a0<\/span><\/td>\n<\/tr>\n
\u2211(x\u1d62 – x\u0304)\u00b2<\/b><\/td>\n 63771,96\u00a0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

I la desviaci\u00f3 est\u00e0ndard \u00e9s de: 52,66 pips (0.0005266 $).<\/span><\/p>\n

Segons la regla emp\u00edrica i de forma aproximada, en una distribuci\u00f3 normal:<\/span><\/p>\n

El 68% de les observacions es troben dins d’una desviaci\u00f3 est\u00e0ndard de la mitjana.<\/span><\/p>\n

El 95% de les observacions es troben dins de dues desviacions est\u00e0ndard de la mitjana.<\/span><\/p>\n

El 99.7% de les observacions es troben dins de tres desviacions est\u00e0ndard de la mitjana.<\/span><\/p>\n

Ara imaginem que ens interessa saber el moviment del preu del EURUSD d\u2019aqu\u00ed un mes si es mantenen les condicions actuals.<\/span><\/p>\n

Per a traslladar la desviaci\u00f3 t\u00edpica d\u2019un per\u00edode a un altre usem l\u2019arrel del per\u00edode.<\/span><\/p>\n

Exemple, si la variaci\u00f3 hor\u00e0ria que hem calculat t\u00e9 una desviaci\u00f3 de 52,66 pips i volem calcular la que podria tenir de forma mensual, multipliquem per un factor que correspon a l\u2019arrel quadrada de les hores que t\u00e9 un mes.<\/span><\/p>\n

Suposant un mes de 30 dies i quatre setmanes, sabent que l\u2019EURUSD haur\u00e0 funcionat els 5 dies feiners tenim que un mes tindr\u00e0 (30 – 4*2) * 24 = 528 hores. Per tant:<\/span><\/p>\n

\"\"<\/p>\n

Per tant, d\u2019aqu\u00ed a un m\u00e9s la possibilitat de que l\u2019EURUSD es mantingui entre els seg\u00fcents valors: 1,08421 \u00b1 0,01210 \u00e9s de 68%.<\/span><\/p>\n

Com veiem, usar la distribuci\u00f3 normal com a aproximaci\u00f3 del moviment de la variaci\u00f3 del preu \u00e9s molt \u00fatil per a fer suposicions.<\/span><\/p>\n

Hem de tenir en compte que he suposat que la mitjana de les variacions del preu de l\u2019EURUSD \u00e9s igual o molt propera a zero. Cosa que implica que considerem el seu moviment com a aleatori (estoc\u00e0stic).<\/span><\/p>\n

La distribuci\u00f3 Lognormal i la volatilitat<\/b><\/p>\n

Si considerem que el moviment dels preus s\u2019acosta a una distribuci\u00f3 lognormal (m\u00e9s que no pas a una distribuci\u00f3 normal) podem deduir que la variaci\u00f3 del logaritme neperi\u00e0 dels preus segueix una distribuci\u00f3 normal.<\/span><\/p>\n

Per tant, si en l\u2019apartat anterior partiem de la difer\u00e8ncia dels preus per a calcular la desviaci\u00f3 est\u00e0ndard, ara partirem de la difer\u00e8ncia dels logaritmes neperians dels preus per a calcular la desviaci\u00f3 est\u00e0ndard.<\/span><\/p>\n

Continuem amb l\u2019exemple anterior:<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Hora<\/b><\/td>\nAsk<\/b><\/td>\nBid<\/b><\/td>\nPreu<\/b><\/td>\nLn Preu<\/b><\/td>\nVariaci\u00f3 hor\u00e0ria<\/b><\/td>\n<\/tr>\n
1:00:00<\/span><\/td>\n1,08117<\/span><\/td>\n1,08115<\/span><\/td>\n1,08116<\/span><\/td>\n0,07803<\/span><\/td>\n0<\/span><\/td>\n<\/tr>\n
2:00:00<\/span><\/td>\n1,08215<\/span><\/td>\n1,08212<\/span><\/td>\n1,08214<\/span><\/td>\n0,07894<\/span><\/td>\n0,00090<\/span><\/td>\n<\/tr>\n
3:00:00<\/span><\/td>\n1,08187<\/span><\/td>\n1,08184<\/span><\/td>\n1,08186<\/span><\/td>\n0,07868<\/span><\/td>\n-0,00026<\/span><\/td>\n<\/tr>\n
4:00:00<\/span><\/td>\n1,08171<\/span><\/td>\n1,08170<\/span><\/td>\n1,08171<\/span><\/td>\n0,07854<\/span><\/td>\n-0,00014<\/span><\/td>\n<\/tr>\n
5:00:00<\/span><\/td>\n1,08140<\/span><\/td>\n1,08137<\/span><\/td>\n1,08139<\/span><\/td>\n0,07824<\/span><\/td>\n-0,00030<\/span><\/td>\n<\/tr>\n
6:00:00<\/span><\/td>\n1,08124<\/span><\/td>\n1,08122<\/span><\/td>\n1,08123<\/span><\/td>\n0,07810<\/span><\/td>\n-0,00014<\/span><\/td>\n<\/tr>\n
7:00:00<\/span><\/td>\n1,08091<\/span><\/td>\n1,08091<\/span><\/td>\n1,08091<\/span><\/td>\n0,07780<\/span><\/td>\n-0,00030<\/span><\/td>\n<\/tr>\n
8:00:00<\/span><\/td>\n1,08127<\/span><\/td>\n1,08126<\/span><\/td>\n1,08127<\/span><\/td>\n0,07813<\/span><\/td>\n0,00033<\/span><\/td>\n<\/tr>\n
9:00:00<\/span><\/td>\n1,08112<\/span><\/td>\n1,08110<\/span><\/td>\n1,08111<\/span><\/td>\n0,07799<\/span><\/td>\n-0,00014<\/span><\/td>\n<\/tr>\n
10:00:00<\/span><\/td>\n1,08162<\/span><\/td>\n1,08156<\/span><\/td>\n1,08159<\/span><\/td>\n0,07843<\/span><\/td>\n0,00044<\/span><\/td>\n<\/tr>\n
11:00:00<\/span><\/td>\n1,08108<\/span><\/td>\n1,08105<\/span><\/td>\n1,08107<\/span><\/td>\n0,07795<\/span><\/td>\n-0,00049<\/span><\/td>\n<\/tr>\n
12:00:00<\/span><\/td>\n1,08189<\/span><\/td>\n1,08187<\/span><\/td>\n1,08188<\/span><\/td>\n0,07870<\/span><\/td>\n0,00075<\/span><\/td>\n<\/tr>\n
13:00:00<\/span><\/td>\n1,08132<\/span><\/td>\n1,08129<\/span><\/td>\n1,08131<\/span><\/td>\n0,07817<\/span><\/td>\n-0,00053<\/span><\/td>\n<\/tr>\n
14:00:00<\/span><\/td>\n1,08129<\/span><\/td>\n1,08127<\/span><\/td>\n1,08128<\/span><\/td>\n0,07815<\/span><\/td>\n-0,00002<\/span><\/td>\n<\/tr>\n
15:00:00<\/span><\/td>\n1,08221<\/span><\/td>\n1,08199<\/span><\/td>\n1,08210<\/span><\/td>\n0,07890<\/span><\/td>\n0,00076<\/span><\/td>\n<\/tr>\n
16:00:00<\/span><\/td>\n1,08356<\/span><\/td>\n1,08354<\/span><\/td>\n1,08355<\/span><\/td>\n0,08024<\/span><\/td>\n0,00134<\/span><\/td>\n<\/tr>\n
17:00:00<\/span><\/td>\n1,08308<\/span><\/td>\n1,08306<\/span><\/td>\n1,08307<\/span><\/td>\n0,07980<\/span><\/td>\n-0,00044<\/span><\/td>\n<\/tr>\n
18:00:00<\/span><\/td>\n1,08379<\/span><\/td>\n1,08376<\/span><\/td>\n1,08378<\/span><\/td>\n0,08045<\/span><\/td>\n0,00065<\/span><\/td>\n<\/tr>\n
19:00:00<\/span><\/td>\n1,08408<\/span><\/td>\n1,08406<\/span><\/td>\n1,08407<\/span><\/td>\n0,08072<\/span><\/td>\n0,00027<\/span><\/td>\n<\/tr>\n
20:00:00<\/span><\/td>\n1,08415<\/span><\/td>\n1,08412<\/span><\/td>\n1,08414<\/span><\/td>\n0,08078<\/span><\/td>\n0,00006<\/span><\/td>\n<\/tr>\n
21:00:00<\/span><\/td>\n1,08374<\/span><\/td>\n1,08373<\/span><\/td>\n1,08374<\/span><\/td>\n0,08041<\/span><\/td>\n-0,00037<\/span><\/td>\n<\/tr>\n
22:00:00<\/span><\/td>\n1,08408<\/span><\/td>\n1,08372<\/span><\/td>\n1,08390<\/span><\/td>\n0,08057<\/span><\/td>\n0,00015<\/span><\/td>\n<\/tr>\n
23:00:00<\/span><\/td>\n1,08407<\/span><\/td>\n1,08395<\/span><\/td>\n1,08401<\/span><\/td>\n0,08067<\/span><\/td>\n0,00010<\/span><\/td>\n<\/tr>\n
0:00:00<\/span><\/td>\n1,08421<\/span><\/td>\n1,08421<\/span><\/td>\n1,08421<\/span><\/td>\n0,08085<\/span><\/td>\n0,00018<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

La variaci\u00f3 hor\u00e0ria \u00e9s la observaci\u00f3 mostral que usarem per a calcular la desviaci\u00f3 est\u00e0ndard.<\/span><\/p>\n

Un apunt, la variaci\u00f3 hor\u00e0ria l\u2019hem calculat a partir de la variaci\u00f3 del logaritme neperi\u00e0 del preu actual i el logaritme neperi\u00e0 del preu anterior. Coneixent el c\u00e0lcul de logaritmes podem deduir que podriem haver calculat la variaci\u00f3 fent el logaritme neperi\u00e0 del preu actual dividit pel preu anterior. I, el m\u00e9s important, el resultat s\u2019assemblaria molt si ho haguessim calculat de la seg\u00fcent manera: Difer\u00e8ncia del preu actual i l\u2019anterior dividit entre la mitjana del preu actual i el preu anterior.<\/span><\/p>\n

En definitiva, la variaci\u00f3 que hem calculat no deixa de ser una variaci\u00f3 en tant per u dels preus (multiplicant per cent tindriem una variaci\u00f3 percentual del preu).<\/span><\/p>\n

Ara en calculem la desviaci\u00f3 est\u00e0ndard usant la f\u00f3rmula que ja coneixem:<\/span>\u00a0\"\"<\/p>\n\n\n\n\n\n\n\n\n
n<\/span><\/td>\n24<\/span><\/td>\n<\/tr>\n
x\u0304<\/span><\/td>\n0,000117378<\/span><\/td>\n<\/tr>\n
\u2211(x\u1d62 – x\u0304)\u00b2<\/b><\/td>\n0,000005445<\/span><\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/tr>\n
s hor\u00e0ria<\/span><\/td>\n0,000486555<\/span><\/td>\n<\/tr>\n
s mensual<\/span><\/td>\n0,01118019203<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

La desviaci\u00f3 est\u00e0ndard d\u2019aquesta distribuci\u00f3 expressada en tant per cent la coneixem com a volatilitat.<\/span><\/p>\n

La desviaci\u00f3 hor\u00e0ria \u00e9s de 0,000486555 i la mensual (multiplicant per l\u2019arrel de 528) \u00e9s de 0,01118. Per tant, i multiplicant per 100, podem dir que la volatilitat hor\u00e0ria \u00e9s de 0.05% i la mensual, de 1,12%.<\/span><\/p>\n

En definitiva, hi ha un 68% de possibilitats que el preu de l\u2019EURUSD s\u2019hagi mogut dins del marge de \u00b11,12% a finals d\u2019aquest mes.<\/span><\/p>\n

Hi ha un 95% de possibilitats que el preu de l\u2019EURUSD s\u2019hagi mogut dins del marge de \u00b12,24% a finals d\u2019aquest mes.<\/span><\/p>\n

Hi ha un 99,7% de possibilitats que el preu de l\u2019EURUSD s\u2019hagi mogut dins del marge de \u00b13,36% a finals d\u2019aquest mes.<\/span><\/p>\n

Quan ens parlen que l\u2019EURUSD t\u00e9 una volatilitat anual de 4% podem fer l\u2019exercici invers al qu\u00e8 hem fet fins ara i averiguar quina volatilitat mensual seria:<\/span><\/p>\n

Volatilitat anual = 4%<\/span><\/p>\n

Volatilitat mensual = Volatilitat anual \/ SQR(12) = 1,15%<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Per a explicar aquest apartat partirem d\u2019un cas pr\u00e0ctic: Agafem com a exemple el moviment de l\u2019EURUSD i triem com a per\u00edode de c\u00e0lcul el d\u2019una hora. Hem de tenir en compte que podriem haver agafat qualsevol per\u00edode per a fer l\u2019exemple (un minut, 5 minuts, una setmana, etc.). Agafem com a preu la mitjana […]<\/p>\n","protected":false},"author":1,"featured_media":25046,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[16],"tags":[],"class_list":["post-24846","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-didactic"],"_links":{"self":[{"href":"https:\/\/qooant.com\/ca\/wp-json\/wp\/v2\/posts\/24846","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/qooant.com\/ca\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qooant.com\/ca\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qooant.com\/ca\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/qooant.com\/ca\/wp-json\/wp\/v2\/comments?post=24846"}],"version-history":[{"count":0,"href":"https:\/\/qooant.com\/ca\/wp-json\/wp\/v2\/posts\/24846\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/qooant.com\/ca\/wp-json\/wp\/v2\/media\/25046"}],"wp:attachment":[{"href":"https:\/\/qooant.com\/ca\/wp-json\/wp\/v2\/media?parent=24846"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qooant.com\/ca\/wp-json\/wp\/v2\/categories?post=24846"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qooant.com\/ca\/wp-json\/wp\/v2\/tags?post=24846"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}