Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 74.81% per annum.
- LRCX price at the close of May 15, 2024 was $947.75 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 23.25% per annum.
- LRCX price at the close of May 15, 2024 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of LRCX price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: September 15, 2022
End date: May 15, 2024
a = 4.0814
b = 0.0015
s = 0.0739
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0015) – 1
= 74.81%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0739) – 1
= 34.41%
September 15, 2022 calculations
Top border of price channel:
Exp(Y840)
= Exp(a + b × X840 + 2 × s)
= Exp(a + b × 1,218 + 2 × s)
= Exp(4.0814 + 0.0015 × 1,218 + 2 × 0.0739)
= Exp(6.0931)
= $442.77
Bottom border of price channel:
Exp(Y840)
= Exp(a + b × X840 – 2 × s)
= Exp(a + b × 1,218 – 2 × s)
= Exp(4.0814 + 0.0015 × 1,218 – 2 × 0.0739)
= Exp(5.7973)
= $329.42
May 15, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.0814 + 0.0015 × 1,826 + 2 × 0.0739)
= Exp(7.0234)
= $1,122.61
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.0814 + 0.0015 × 1,826 – 2 × 0.0739)
= Exp(6.7277)
= $835.23
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 74.81% per annum.
- LRCX price at the close of May 15, 2024 was $947.75 and was inside the primary price channel.
Secondary Trend
Start date: February 22, 2024
End date: May 15, 2024
a = 8.1367
b = -0.0007
s = 0.0315
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -23.25%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0315) – 1
= 13.42%
February 22, 2024 calculations
Top border of price channel:
Exp(Y1,200)
= Exp(a + b × X1,200 + 2 × s)
= Exp(a + b × 1,743 + 2 × s)
= Exp(8.1367 + -0.0007 × 1,743 + 2 × 0.0315)
= Exp(6.9357)
= $1,028.39
Bottom border of price channel:
Exp(Y1,200)
= Exp(a + b × X1,200 – 2 × s)
= Exp(a + b × 1,743 – 2 × s)
= Exp(8.1367 + -0.0007 × 1,743 – 2 × 0.0315)
= Exp(6.8098)
= $906.71
May 15, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(8.1367 + -0.0007 × 1,826 + 2 × 0.0315)
= Exp(6.8756)
= $968.32
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(8.1367 + -0.0007 × 1,826 – 2 × 0.0315)
= Exp(6.7496)
= $853.75
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 23.25% per annum.
- LRCX price at the close of May 15, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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